000			06307cam a2200661Mi 4500
001			on1004831978
003			OCoLC
005			20220517104404.0
006			m d
007			cr |n|||||||||
008			170928s2015 fr a gob 001 0 fre d
040			_aYDX _beng _epn _erda _cYDX _dEBLCP _dIDB _dN$T _dOCLCQ _dEZ9 _dOCLCO _dOCLCF _dOCLCQ _dOCLCO _dCUY _dLOA _dZCU _dMERUC _dICG _dCOCUF _dDKC _dUX1 _dUKKNU
020			_a9782759819522 _q(electronic bk.)
020			_a2759819523 _q(electronic bk.)
020			_a9782759817382 _q(electronic bk.)
020			_a2759817385 _q(electronic bk.)
035			_a1605172 _b(N$T)
035			_a(OCoLC)1004831978
037			_a102204 _bKnowledge Unlatched
050		4	_aQA171.5 _b.Z455 2015eb
072		7	_aMAT _x000000 _2bisacsh
072		7	_aPHM _2bicssc
082	0	4	_a511.33 _223
049			_aMAIN
100	1		_aZhilinskii, Boris, _eauthor _932571
245	1	0	_aIntroduction to Louis Michel's lattice geometry through group action / _cBoris Zhilinskii, Michel Leduc, Michel Le Bellac.
264		1	_aLes Ulis : _bEDP sciences, _c2015.
264		4	_c©2015
300			_a1 online resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	0		_aCurrent Natural Sciences
505	0		_aIntroduction to Louis Michel's lattice geometry through group action; Contents; Preface; 1 -- Introduction; 2 -- Group action. Basic definitions and examples; 2.1 The action of a group on itself; 2.2 Group action on vector space; 3 -- Delone sets and periodic lattices; 3.1 Delone sets; 3.2 Lattices; 3.3 Sublattices of L; 3.4 Dual lattices; 4 -- Lattice symmetry; 4.1 Introduction; 4.2 Point symmetry of lattices; 4.3 Bravais classes; 4.4 Correspondence between Bravais classes and lattice point symmetry groups; 4.5 Symmetry, stratification, and fundamental domains.
505	8		_a4.6 Point symmetry of higher dimensional lattices5 -- Lattices and their Voronoïand Delone cells; 5.1 Tilings by polytopes: some basic concepts; 5.2 Voronoï cells and Delone polytopes; 5.3 Duality; 5.4 Voronoï and Delone cells of point lattices; 5.5 Classification of corona vectors; 6 -- Lattices and positive quadratic forms; 6.1 Introduction; 6.2 Two dimensional quadratic forms and lattices; 6.3 Three dimensional quadratic forms and 3D-lattices; 6.4 Parallelohedra and cells for N-dimensional lattices; 6.5 Partition of the cone of positive-definite quadratic forms.
505	8		_a6.6 Zonotopes and zonohedral families of parallelohedra6.7 Graphical visualization of members of the zonohedral family; 6.8 Graphical visualization of non-zonohedral lattices; 6.9 On Voronoï conjecture; 7 -- Root systems and root lattices; 7.1 Root systems of lattices and root lattices; 7.2 Lattices of the root systems; 7.3 Low dimensional root lattices; 8 -- Comparison of lattice classifications; 8.1 Geometric and arithmetic classes; 8.2 Crystallographic classes; 8.3 Enantiomorphism; 8.4 Time reversal invariance; 8.5 Combining combinatorial and symmetry classification; 9 -- Applications.
505	8		_a9.1 Sphere packing, covering, and tiling9.2 Regular phases of matter; 9.3 Quasicrystals; 9.4 Lattice defects; 9.5 Lattices in phase space. Dynamical models. Defects; 9.6 Modular group; 9.7 Lattices and Morse theory; A -- Basic notions of group theory with illustrative examples; B -- Graphs, posets, and topological invariants; C -- Notations for point and crystallographic groups; C.1 Two-dimensional point groups; C.2 Crystallographic plane and space groups; C.3 Notation for four-dimensional parallelohedra; D -- Orbit spaces for planecrystallographic groups.
505	8		_aE -- Orbit spaces for 3D-irreducible Bravais groupsBibliography; Index.
504			_aIncludes bibliographical references and index.
520	8		_aAnnotation _bGroup action analysis developed and applied mainly by Louis Michel to the study of N-dimensional periodic lattices is the main subject of the book. Different basic mathematical tools currently used for the description of lattice geometry are introduced and illustrated through applications to crystal structures in two- and three-dimensional space, to abstract multi-dimensional lattices and to lattices associated with integrable dynamical systems. Starting from general Delone sets authors turn to different symmetry and topological classifications including explicit construction of orbifolds for two- and three-dimensional point and space groups. Voronoi and Delone cells together with positive quadratic forms and lattice description by root systems are introduced to demonstrate alternative approaches to lattice geometry study. Zonotopes and zonohedral families of 2-, 3-, 4-, 5-dimensional lattices are explicitly visualized using graph theory approach. Along with crystallographic applications, qualitative features of lattices of quantum states appearing for quantum problems associated with classical Hamiltonian integrable dynamical systems are shortly discussed. The presentation of the material is done through a number of concrete examples with an extensive use of graphical visualization. The book is addressed to graduated and post-graduate students and young researches in theoretical physics, dynamical systems, applied mathematics, solid state physics, crystallography, molecular physics, theoretical chemistry, ..."
542	1		_fThis work is licensed under a Creative Commons license _uhttps://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
590			_aMaster record variable field(s) change: 072
650		0	_aLattice theory. _932572
650		7	_aMATHEMATICS _xGeneral. _2bisacsh
650		7	_aLattice theory. _2fast _0(OCoLC)fst00993426 _932572
650		7	_aAtomic & molecular physics _2bicssc _925310
655		4	_aElectronic books.
700	1		_aLeduc, Michel. _932573
700	1		_aLe Bellac, Michel. _932574
776	0	8	_iPrint version: _z9782759817382 _z2759817385 _w(OCoLC)936210752
856	4	0	_3EBSCOhost _uhttps://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=1605172
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938			_aEBSCOhost _bEBSC _n1605172
938			_aYBP Library Services _bYANK _n14818064
942			_cEBK
994			_a92 _bN$T
999			_c5600 _d5600