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001482836 001__ 1482836
001482836 003__ OCoLC
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001482836 019__ $$a1407277760
001482836 020__ $$a9789819957699$$q(electronic bk.)
001482836 020__ $$a9819957699$$q(electronic bk.)
001482836 020__ $$z9819957680
001482836 020__ $$z9789819957682
001482836 0247_ $$a10.1007/978-981-99-5769-9$$2doi
001482836 035__ $$aSP(OCoLC)1407315307
001482836 040__ $$aEBLCP$$beng$$cEBLCP$$dYDX$$dGW5XE$$dOCLCO
001482836 049__ $$aISEA
001482836 050_4 $$aQD911
001482836 08204 $$a548.7$$223/eng/20231114
001482836 1001_ $$aNaito, Hisashi,$$d1961-
001482836 24510 $$aTrivalent discrete surfaces and carbon structures /$$cHisashi Naito.
001482836 260__ $$aSingapore :$$bSpringer,$$c2023.
001482836 300__ $$a1 online resource (113 p.).
001482836 4901_ $$aSpringerBriefs in the Mathematics of Materials ;$$vv. 5
001482836 5050_ $$aIntro -- Preface -- Contents -- 1 Overview of This Monograph -- 2 Graph Theory -- 2.1 Graph -- 2.2 Covering Graph -- 2.3 Graph Laplacian -- 3 Topological Crystals -- 3.1 Topological Crystals and Their Standard Realizations -- 3.2 Construction of Standard Realizations -- 3.2.1 Explicit Calculations in Cases of Maximal Abelian Coverings -- 3.2.2 Explicit Calculations for Generic Cases -- 3.3 Carbon Structures and Standard Realizations -- 4 Negatively Curved Carbon Structures -- 4.1 Carbon Structures as Discrete Surfaces -- 4.2 Constructions of Negatively Curved Carbon Structures ...
001482836 5058_ $$a5 Trivalent Discrete Surfaces -- 5.1 Curvatures of Trivalent Discrete Surfaces -- 5.2 Examples of Trivalent Discrete Surfaces and Their Curvatures -- 5.3 Construction of Trivalent Minimal Discrete Surfaces -- 6 Subdivisions of Trivalent Discrete Surfaces -- 6.1 Goldberg-Coxeter Constructions -- 6.2 Subdivisions of Trivalent Discrete Surfaces -- 6.3 Another Method of Subdivision of Trivalent Discrete Surfaces -- 7 Miscellaneous Topics -- 7.1 Carbon Nanotubes from Geometric Viewpoints -- 7.2 Material Properties and Discrete Geometry
001482836 5058_ $$a7.3 Graph Spectra and Electronic Properties of Carbon Structures -- 7.3.1 The Hückel Method -- 7.3.2 Tight-Binding Approximations -- 7.3.3 The Density Function Theory -- 7.4 Eigenvalues of Subdivisions of Trivalent Discrete Surfaces -- 7.5 Graph Algorithms and Miscellaneous Computation Methods -- 7.5.1 Graph Algorithms -- 7.5.2 Numerical Methods for Matrices -- Appendix References -- Index
001482836 506__ $$aAccess limited to authorized users.
001482836 520__ $$aThis book discusses discrete geometric analysis, especially topological crystallography and discrete surface theory for trivalent discrete surfaces. Topological crystallography, based on graph theory, provides the most symmetric structure among given combinatorial structures by using the variational principle, and it can reproduce crystal structures existing in nature. In this regard, the topological crystallography founded by Kotani and Sunada is explained by using many examples. Carbon structures such as fullerenes are considered as trivalent discrete surfaces from the viewpoint of discrete geometric analysis. Discrete surface theories usually have been considered discretization of smooth surfaces. Here, consideration is given to discrete surfaces modeled by crystal/molecular structures, which are essentially discrete objects. .
001482836 650_6 $$aCristallographie mathématique.
001482836 650_6 $$aCarbone$$xStructure$$xModèles mathématiques.
001482836 650_6 $$aCarbone$$xComposés$$xStructure$$xModèles mathématiques.
001482836 650_6 $$aGéométrie discrète.
001482836 650_0 $$aCrystallography, Mathematical.
001482836 650_0 $$aCarbon$$xStructure$$xMathematical models.
001482836 650_0 $$aCarbon compounds$$xStructure$$xMathematical models.$$0(DLC)sh 85020102
001482836 650_0 $$aSurfaces.
001482836 650_0 $$aDiscrete geometry.$$0(DLC)sh2002004432
001482836 655_0 $$aElectronic books.
001482836 77608 $$iPrint version:$$aNaito, Hisashi$$tTrivalent Discrete Surfaces and Carbon Structures$$dSingapore : Springer,c2023$$z9789819957682
001482836 830_0 $$aSpringerBriefs in the mathematics of materials ;$$vv. 5.
001482836 852__ $$bebk
001482836 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-99-5769-9$$zOnline Access$$91397441.1
001482836 909CO $$ooai:library.usi.edu:1482836$$pGLOBAL_SET
001482836 980__ $$aBIB
001482836 980__ $$aEBOOK
001482836 982__ $$aEbook
001482836 983__ $$aOnline
001482836 994__ $$a92$$bISE