05206nam 2200637 450 991083022970332120210617135051.01-119-02387-40-470-54909-2(CKB)2480000000008325(EBL)698730(SSID)ssj0000481496(PQKBManifestationID)11324744(PQKBTitleCode)TC0000481496(PQKBWorkID)10471312(PQKB)10410401(MiAaPQ)EBC698730(MiAaPQ)EBC4945124(PPN)189305347(OCoLC)587063574(EXLCZ)99248000000000832520180206h20102010 uy 0engur|n|---|||||txtccrGeographic information analysis /David O'Sullivan and David J. Unwin2nd ed.Hoboken, New Jersey :Wiley,2010.©20101 online resource (431 p.)Description based upon print version of record.0-470-28857-4 Includes bibliographical references and index.Geographic Information Analysis; Contents; Preface to the Second Edition; Acknowledgments; Preface to the First Edition; 1 Geographic Information Analysis and Spatial Data; Chapter Objectives; 1.1 Introduction; 1.2 Spatial Data Types; The Object View; The Field View; Choosing the Representation to Be Used; Types of Spatial Object; 1.3 Some Complications; Objects Are Not Always What They Appear to Be; Objects Are Usually Multidimensional; Objects Don't Move or Change; Objects Don't Have Simple Geometries; Objects Depend on the Scale of Analysis; Objects Might Have Fractal DimensionObjects Can Be Fuzzy and/or Have Indeterminate Boundaries1.4 Scales for Attribute Description; Nominal Measures; Ordinal Measures; Interval and Ratio Measures; Dimensions and Units; 1.5 GIS and Spatial Data Manipulation; 1.6 The Road Ahead; Chapter Review; References; 2 The Pitfalls and Potential of Spatial Data; Chapter Objectives; 2.1 Introduction; 2.2 The Bad News: The Pitfalls of Spatial Data; Spatial Autocorrelation; The Modifiable Areal Unit Problem; The Ecological Fallacy; Scale; Nonuniformity of Space and Edge Effects; 2.3 The Good News: The Potential of Spatial Data; DistanceAdjacencyInteraction; Neighborhood; Summarizing Relationships in Matrices; Proximity Polygons; Chapter Review; References; 3 Fundamentals-Mapping It Out; Chapter Objectives; 3.1 Introduction: The Cartographic Tradition; 3.2 Geovisualization and Analysis; 3.3 The Graphic Variables of Jacques Bertin; 3.4 New Graphic Variables; Animation and Graphics Scripts; Linking and Brushing; Projection; 3.5 Issues in Geovisualization; 3.6 Mapping and Exploring Points; Dot or Pin Maps; Kernel Density Maps; Located Proportional Symbol Maps; 3.7 Mapping and Exploring Areas; Color Patch Maps; Choropleth MapsClassless ChoroplethsMaps of Relative Rates; Dasymetric Mapping; Surface Models for Area Objects; Area Cartograms; 3.8 Mapping and Exploring Fields; Point Values: Spot Heights, Benchmarks, and Bubble Plots; Contours and Isolines; Enhancing the Isoline; Other Ways of Displaying Surfaces; 3.9 The Spatialization of Nonspatial Data; 3.10 Conclusion; Chapter Review; References; 4 Fundamentals-Maps as Outcomes of Processes; Chapter Objectives; 4.1 Introduction: Maps and Processes; 4.2 Processes and the Patterns They Make; Deterministic Processes; A Stochastic Process and Its Realizations4.3 Predicting the Pattern Generated by a Process4.4 More Definitions; 4.5 Stochastic Processes in Lines, Areas, and Fields; Line Objects; Area Objects; Fields; 4.6 Conclusions; Chapter Review; References; 5 Point Pattern Analysis; Chapter Objectives; 5.1 Introduction; 5.2 Describing a Point Pattern; Centrography; Density-Based Point Pattern Measures; Quadrat Count Methods; Distance-Based Point Pattern Measures; Edge Effects; 5.3 Assessing Point Patterns Statistically; Quadrat Counts; Nearest-Neighbor Distances; The G and F Functions; The K Function; 5.4 Monte Carlo Testing; 5.5 ConclusionsChapter Review<i>Geographic Information Analysis </i>provides up-to-date coverage of the foundations of spatial data analysis through visualization and maps. This book covers key spatial concepts, including point pattern, line objects and networks, area objects, and continuous fields, as well as such new subjects as local statistics. With crucial methods for analyzing geographical information, this is an essential reference for professionals as well as a useful text for the classroom. <br />Geographic information systemsSpatial analysis (Statistics)Geographic information systems.Spatial analysis (Statistics)910.285O'Sullivan David1966-1638505Unwin D(David John),MiAaPQMiAaPQMiAaPQBOOK9910830229703321Geographic information analysis3980985UNINA11261nam 22007335 450 991096703240332120250818100347.03-642-80021-110.1007/978-3-642-80021-4(CKB)3400000000108467(SSID)ssj0000806511(PQKBManifestationID)11492833(PQKBTitleCode)TC0000806511(PQKBWorkID)10747259(PQKB)11442843(DE-He213)978-3-642-80021-4(MiAaPQ)EBC3096373(PPN)23808163X(EXLCZ)99340000000010846720121227d1990 u| 0engurnn|008mamaatxtccrGroup Theory and Its Applications in Physics /by Teturo Inui, Yukito Tanabe, Yositaka Onodera1st ed. 1990.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,1990.1 online resource (XV, 397 p.) Springer Series in Solid-State Sciences,2197-4179 ;78"With 72 Figures."3-540-19105-4 3-540-60445-6 Includes bibliographical references and index.1. Symmetry and the Role of Group Theory -- 1.1 Arrangement of the Book -- 2. Groups -- 2.1 Definition of a Group -- 2.1.1 Multiplication Tables -- 2.1.2 Generating Elements -- 2.1.3 Commutative Groups -- 2.2 Covering Operations of Regular Polygons -- 2.3 Permutations and the Symmetric Group -- 2.4 The Rearrangement Theorem -- 2.5 Isomorphism and Homomorphism -- 2.5.1 Isomorphism -- 2.5.2 Homomorphism -- 2.5.3 Note on Mapping -- 2.6 Subgroups -- 2.7 Cosets and Coset Decomposition -- 2.8 Conjugate Elements; Classes -- 2.9 Multiplication of Classes -- 2.10 Invariant Subgroups -- 2.11 The Factor Group -- 2.11.1 The Kernel -- 2.11.2 Homomorphism Theorem -- 2.12 The Direct-Product Group -- 3. Vector Spaces -- 3.1 Vectors and Vector Spaces -- 3.1.1 Mathematical Definition of a Vector Space -- 3.1.2 Basis of a Vector Space -- 3.2 Transformation of Vectors -- 3.3 Subspaces and Invariant Subspaces -- 3.4 Metric Vector Spaces -- 3.4.1 Inner Product of Vectors -- 3.4.2 Orthonormal Basis -- 3.4.3 Unitary Operators and Unitary Matrices -- 3.4.4 Hermitian Operators and Hermitian Matrices -- 3.5 Eigenvalue Problems of Hermitian and Unitary Operators -- 3.6 Linear Transformation Groups -- 4. Representations of a Group I -- 4.1 Representations -- 4.1.1 Basis for a Representation -- 4.1.2 Equivalence of Representations -- 4.1.3 Reducible and Irreducible Representations -- 4.2 Irreducible Representations of the Group C?v -- 4.3 Effect of Symmetry Transformation Operators on Functions -- 4.4 Representations of the Group C3v Based on Homogeneous Polynomials -- 4.5 General Representation Theory -- 4.5.1 Unitarization of a Representation -- 4.5.2 Schur’s First Lemma -- 4.5.3 Schur’s Second Lemma -- 4.5.4 The Great Orthogonality Theorem T -- 4.6 Characters -- 4.6.1 First and Second Orthogonalities of Characters -- 4.7 Reduction ofReducible Representations -- 4.7.1 Restriction to a Subgroup -- 4.8 Product Representations -- 4.8.1 Symmetric and Antisymmetric Product Representations -- 4.9 Representations of a Direct-Product Group -- 4.10 The Regular Representation -- 4.11 Construction of Character Tables -- 4.12 Adjoint Representations -- 4.13 Proofs of the Theorems on Group Representations -- 4.13.1 Unitarization of a Representation -- 4.13.2 Schur’s First Lemma -- 4.13.3 Schur’s Second Lemma -- 4.13.4 Second Orthogonality of Characters -- 5. Representations of a Group II -- 5.1 Induced Representations -- 5.2 Irreducible Representations of a Group with an Invariant Subgroup -- 5.3 Irreducible Representations of Little Groups or Small Representations -- 5.4 Ray Representations -- 5.5 Construction of Matrices of Irreducible Ray Representations -- 6. Group Representations in Quantum Mechanics -- 6.1 Symmetry Transformations of Wavefunctions and Quantum-Mechanical Operators -- 6.2 Eigenstates of the Hamiltonian and Irreducibility -- 6.3 Splitting of Energy Levels by a Perturbation -- 6.4 Orthogonality of Basis Functions -- 6.5 Selection Rules -- 6.5.1 Derivation of the Selection Rule for Diagonal Matrix Elements -- 6.6 Projection Operators -- 7. The Rotation Group -- 7.1 Rotations -- 7.2 Rotation and Euler Angles -- 7.3 Rotations as Operators; Infinitesimal Rotations -- 7.4 Representation of Infinitesimal Rotations -- 7.4.1 Rotation of Spin Functions -- 7.5 Representations of the Rotation Group -- 7.6 SU(2), SO(3) and O(3) -- 7.7 Basis of Representations -- 7.8 Spherical Harmonics -- 7.9 Orthogonality of Representation Matrices and Characters -- 7.9.1 Completeness Relation for XJ(?) -- 7.10 Wigner Coefficients -- 7.11 Tensor Operators -- 7.12 Operator Equivalents -- 7.13 Addition of Three Angular Momenta;Racah Coefficients -- 7.14Electronic Wavefunctions for the Configuration (nl)x -- 7.15 Electrons and Holes -- 7.16 Evaluation of the Matrix Elements of Operators -- 8. Point Groups -- 8.1 Symmetry Operations in Point Groups -- 8.2 Point Groups and Their Notation -- 8.3 Class Structure in Point Groups -- 8.4 Irreducible Representations of Point Groups -- 8.5 Double-Valued Representations and Double Groups -- 8.6 Transformation of Spin and Orbital Functions -- 8.7 Constructive Derivation of Point Groups Consisting of Proper Rotations -- 9. Electronic States of Molecules -- 9.1 Molecular Orbitals -- 9.2 Diatomic Molecules: LCAO Method -- 9.3 Construction of LCAO-MO: The ?-Electron Approximation for the Benzene Molecule -- 9.3.1 Further Methods for Determining the Basis Sets -- 9.4 The Benzene Molecule (Continued) -- 9.5 Hybridized Orbitals -- 9.5.1 Methane and sp3-Hybridization -- 9.6 Ligand Field Theory -- 9.7 Multiplet Terms in Molecules -- 9.8 Clebsch - Gordan Coefficients for Simply Reducible Groups and the Wigner-Eckart Theorem -- 10. Molecular Vibrations -- 10.1 Normal Modes and Normal Coordinates -- 10.2 Group Theory and Normal Modes -- 10.3 Selection Rules for Infrared Absorption and Raman Scattering -- 10.4 Interaction of Electrons with Atomic Displacements -- 10.4.1 Kramers Degeneracy -- 11. Space Groups -- 11.1 Translational Symmetry of Crystals -- 11.2 Symmetry Operations in Space Groups -- 11.3 Structure of Space Groups -- 11.4 Bravais Lattices -- 11.5 Nomenclature of Space Groups -- 11.6 The Reciprocal Lattice and the Brillouin Zone -- 11.7 Irreducible Representations of the Translation Group… -- 11.8 The Group of the Wavevector k and Its Irreducible Representations -- 11.9 Irreducible Representations of a Space Group -- 11.10 Double Space Groups -- 12. Electronic States in Crystals -- 12.1 Bloch Functions and E(k)Spectra -- 12.2 Examples of Energy Bands: Ge and TIBr -- 12.3 Compatibility or Connectivity Relations -- 12.4 Bloch Functions Expressed in Terms of Plane Waves -- 12.5 Choice of the Origin -- 12.5.1 Effect of the Choice on Bloch Wavefunctions -- 12.6 Bloch Functions Expressed in Terms of Atomic Orbitals -- 12.7 Lattice Vibrations -- 12.8 The Spin-Orbit Interaction and Double Space Groups…. -- 12.9 Scattering of an Electron by Lattice Vibrations -- 12.10 Interband Optical Transitions -- 12.11 Frenkel Excitons in Molecular Crystals -- 12.12 Selection Rules in Space Groups -- 12.12.1 Symmetric and Antisymmetric Product Representations -- 13. Time Reversal and Nonunitary Groups -- 13.1 Time Reversal -- 13.2 Nonunitary Groups and Corepresentations -- 13.3 Criteria for Space Groups and Examples -- 13.4 Magnetic Space Groups -- 13.5 Excitons in Magnetic Compounds; Spin Waves -- 13.5.1 Symmetry of the Hamiltonian -- 14. Landau’s Theory of Phase Transitions -- 14.1 Landau’s Theory of Second-Order Phase Transitions -- 14.2 Crystal Structures and Spin Alignments -- 14.3 Derivation of the Lifshitz Criterion -- 14.3.1 Lifshitz’s Derivation of the Lifshitz Criterion -- 15. The Symmetric Group -- 15.1 The Symmetric Group (Permutation Group) -- 15.2 Irreducible Characters -- 15.3 Construction of Irreducible Representation Matrices -- 15.4 The Basis for Irreducible Representations -- 15.5 The Unitary Group and the Symmetric Group -- 15.6 The Branching Rule -- 15.7 Wavefunctions for the Configuration (nl)x -- 15.8 D(J) as Irreducible Representations of SU(2) -- 15.9 Irreducible Representations of U(m) -- Appendices -- A. The Thirty-Two Crystallographic Point Groups -- B. Character Tables for Point Groups -- Answers and Hints to the Exercises -- Motifs of the Family Crests -- References.This book has been written to introduce readers to group theory and its ap­ plications in atomic physics, molecular physics, and solid-state physics. The first Japanese edition was published in 1976. The present English edi­ tion has been translated by the authors from the revised and enlarged edition of 1980. In translation, slight modifications have been made in. Chaps. 8 and 14 to update and condense the contents, together with some minor additions and improvements throughout the volume. The authors cordially thank Professor J. L. Birman and Professor M. Car­ dona, who encouraged them to prepare the English translation. Tokyo, January 1990 T. Inui . Y. Tanabe Y. Onodera Preface to the Japanese Edition As the title shows, this book has been prepared as a textbook to introduce readers to the applications of group theory in several fields of physics. Group theory is, in a nutshell, the mathematics of symmetry. It has three main areas of application in modern physics. The first originates from early studies of crystal morphology and constitutes a framework for classical crystal physics. The analysis of the symmetry of tensors representing macroscopic physical properties (such as elastic constants) belongs to this category. The sec­ ond area was enunciated by E. Wigner (1926) as a powerful means of handling quantum-mechanical problems and was first applied in this sense to the analysis of atomic spectra. Soon, H.Springer Series in Solid-State Sciences,2197-4179 ;78Mathematical physicsCrystallographyAtomsMoleculesMathematical Methods in PhysicsTheoretical, Mathematical and Computational PhysicsCrystallography and Scattering MethodsAtomic, Molecular and Chemical PhysicsMathematical physics.Crystallography.Atoms.Molecules.Mathematical Methods in Physics.Theoretical, Mathematical and Computational Physics.Crystallography and Scattering Methods.Atomic, Molecular and Chemical Physics.530.1/522Inui Teturoauthttp://id.loc.gov/vocabulary/relators/aut1846399Tanabe Yukitoauthttp://id.loc.gov/vocabulary/relators/autOnodera Yositakaauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910967032403321Group Theory and Its Applications in Physics4430845UNINA