{"product_id":"chebyshev-and-fourier-spectral-methods-revised","title":"Chebyshev and Fourier Spectral Methods (Revised)","description":"\n\u003ctable align=\"center\" border=\"0\" cellpadding=\"2\" cellspacing=\"0\" width=\"100%\"\u003e\n\u003ctr\u003e\n\u003ctd class=\"productDetailSmallElements\"\u003e\n\u003cp\u003e\n\u003cstrong\u003eTable of Contents\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tPreface; Acknowledgments; Errata and Extended-Bibliography \n\u003cbr\u003e1. Introduction \n\u003cbr\u003e 1.1 Series expansions \n\u003cbr\u003e 1.2 First example \n\u003cbr\u003e 1.3 Comparison with finite element methods \n\u003cbr\u003e 1.4 Comparisons with finite differences \n\u003cbr\u003e 1.5 Parallel computers \n\u003cbr\u003e 1.6 Choice of basis functions \n\u003cbr\u003e 1.7 Boundary conditions \n\u003cbr\u003e 1.8 Non-Interpolating and Pseudospectral \n\u003cbr\u003e 1.9 Nonlinearity \n\u003cbr\u003e 1.10 Time-dependent problems \n\u003cbr\u003e 1.11 FAQ: frequently asked questions \n\u003cbr\u003e 1.12 The chrysalis \n\u003cbr\u003e2. Chebyshev \u0026amp; Fourier series \n\u003cbr\u003e 2.1 Introduction \n\u003cbr\u003e 2.2 Fourier series \n\u003cbr\u003e 2.3 Orders of convergence \n\u003cbr\u003e 2.4 Convergence order \n\u003cbr\u003e 2.5 Assumption of equal errors \n\u003cbr\u003e 2.6 Darboux's principle \n\u003cbr\u003e 2.7 Why Taylor series fail \n\u003cbr\u003e 2.8 Location of singularities \n\u003cbr\u003e 2.8.1 Corner singularities \u0026amp; compatibility conditions \n\u003cbr\u003e 2.9 FACE: Integration-by-Parts bound \n\u003cbr\u003e 2.10 Asymptotic calculation of Fourier coefficients \n\u003cbr\u003e 2.11 Convergence theory: Chebyshev polynomials \n\u003cbr\u003e 2.12 Last coefficient rule-of-thumb \n\u003cbr\u003e 2.13 Convergence theory for Legendre polynomials \n\u003cbr\u003e 2.14 Quasi-Sinusoidal rule of thumb \n\u003cbr\u003e 2.15 Witch of Agensi rule-of-thumb \n\u003cbr\u003e 2.16 Boundary layer rule-of-thumb \n\u003cbr\u003e3. Galerkin \u0026amp; Weighted residual methods \n\u003cbr\u003e 3.1 Mean weighted residual methods \n\u003cbr\u003e 3.2 Completeness and boundary conditions \n\u003cbr\u003e 3.3 Inner product \u0026amp; orthogonality \n\u003cbr\u003e 3.4 Galerkin method \n\u003cbr\u003e 3.5 Integration-by-Parts \n\u003cbr\u003e 3.6 Galerkin method: case studies \n\u003cbr\u003e 3.7 Separation-of-Variables \u0026amp; the Galerkin method \n\u003cbr\u003e 3.8 Heisenberg Matrix mechanics \n\u003cbr\u003e 3.9 The Galerkin method today \n\u003cbr\u003e4. Interpolation, collocation \u0026amp; all that \n\u003cbr\u003e 4.1 Introduction \n\u003cbr\u003e 4.2 Polynomial interpolation \n\u003cbr\u003e 4.3 Gaussian integration \u0026amp; pseudospectral grids \n\u003cbr\u003e 4.4 Pseudospectral Is Galerkin method via Quadrature \n\u003cbr\u003e 4.5 Pseudospectral errors \n\u003cbr\u003e5. Cardinal functions \n\u003cbr\u003e 5.1 Introduction \n\u003cbr\u003e 5.2 Whittaker cardinal or \"sinc\" functions \n\u003cbr\u003e 5.3 Trigonometric interpolation \n\u003cbr\u003e 5.4 Cardinal functions for orthogonal polynomials \n\u003cbr\u003e 5.5 Transformations and interpolation \n\u003cbr\u003e6. Pseudospectral methods for BVPs \n\u003cbr\u003e 6.1 Introduction \n\u003cbr\u003e 6.2 Choice of basis set \n\u003cbr\u003e 6.3 Boundary conditions: behavioral \u0026amp; numerical \n\u003cbr\u003e 6.4 \"Boundary-bordering\" \n\u003cbr\u003e 6.5 \"Basis Recombination\" \n\u003cbr\u003e 6.6 Transfinite interpolation \n\u003cbr\u003e 6.7 The Cardinal function basis \n\u003cbr\u003e 6.8 The interpolation grid \n\u003cbr\u003e 6.9 Computing basis functions \u0026amp; derivatives \n\u003cbr\u003e 6.10 Higher dimensions: indexing \n\u003cbr\u003e 6.11 Higher dimensions \n\u003cbr\u003e 6.12 Corner singularities \n\u003cbr\u003e 6.13 Matrix methods \n\u003cbr\u003e 6.14 Checking \n\u003cbr\u003e 6.15 Summary \n\u003cbr\u003e7. Linear eigenvalue problems \n\u003cbr\u003e 7.1 The No-brain method \n\u003cbr\u003e 7.2 QR\/QZ Algorithm \n\u003cbr\u003e 7.3 Eigenvalue rule-of-thumb \n\u003cbr\u003e 7.4 Four kinds of Sturm-Liouville problems \n\u003cbr\u003e 7.5 Criteria for Rejecting eigenvalues \n\u003cbr\u003e 7.6 \"Spurious\" eigenvalues \n\u003cbr\u003e 7.7 Reducing the condition number \n\u003cbr\u003e 7.8 The power method \n\u003cbr\u003e 7.9 Inverse power method \n\u003cbr\u003e 7.10 Combining global \u0026amp; local methods \n\u003cbr\u003e 7.11 Detouring into the complex plane \n\u003cbr\u003e 7.12 Common errors \n\u003cbr\u003e8. Symmetry \u0026amp; parity \n\u003cbr\u003e 8.1 Introduction \n\u003cbr\u003e 8.2 Parity \n\u003cbr\u003e 8.3 Modifying the Grid to Exploit parity \n\u003cbr\u003e 8.4 Other discrete symmetries \n\u003cbr\u003e 8.5 Axisymmetric \u0026amp; apple-slicing models \n\u003cbr\u003e9. Explicit time-integration methods \n\u003cbr\u003e 9.1 Introduction \n\u003cbr\u003e 9.2 Spatially-varying coefficients \n\u003cbr\u003e 9.3 The Shamrock principle \n\u003cbr\u003e 9.4 Linear and nonlinear \n\u003cbr\u003e 9.5 Example: KdV equation \n\u003cbr\u003e 9.6 Implicitly-Implicit: RLW \u0026amp; QG \n\u003cbr\u003e10. Partial summation, the FFT and MMT \n\u003cbr\u003e 10.1 Introduction \n\u003cbr\u003e 10.2 Partial summation \n\u003cbr\u003e 10.3 The fast Fourier transform: theory \n\u003cbr\u003e 10.4 Matrix multiplication transform \n\u003cbr\u003e 10.5 Costs of the fast Fourier transform \n\u003cbr\u003e 10.6 Generalized FFTs and multipole methods \n\u003cbr\u003e 10.7 Off-grid interpolation \n\u003cbr\u003e 10.8 Fast Fourier transform: practical matters \n\u003cbr\u003e 10.9 Summary \n\u003cbr\u003e11. Aliasing, spectral blocking, \u0026amp; blow-up \n\u003cbr\u003e 11.1 Introduction \n\u003cbr\u003e 11.2 Aliasing and Equality-on-the-grid \n\u003cbr\u003e 11.3 \"2 h-Waves\" and spectral blocking \n\u003cbr\u003e 11.4 Aliasing instability: history and remedies \n\u003cbr\u003e 11.5 Dealiasing and the Orszag two-thirds rule \n\u003cbr\u003e 11.6 Energy-conserving: constrained interpolation \n\u003cbr\u003e 11.7 Energy-conserving schemes: discussion \n\u003cbr\u003e 11.8 Aliasing instability: theory \n\u003cbr\u003e 11.9 Summary \n\u003cbr\u003e12. Implicit schemes \u0026amp; the slow manifold \n\u003cbr\u003e 12.1 Introduction \n\u003cbr\u003e 12.2 Dispersion and amplitude errors \n\u003cbr\u003e 12.3 Errors \u0026amp; CFL limit for explicit schemes \n\u003cbr\u003e 12.4 Implicit time-marching algorithms \n\u003cbr\u003e 12.5 Semi-implicit methods \n\u003cbr\u003e 12.6 Speed-reduction rule-of-thumb \n\u003cbr\u003e 12.7 Slow manifold: meteorology \n\u003cbr\u003e 12.8 Slow manifold: definition \u0026amp; examples \n\u003cbr\u003e 12.9 Numerically-induced slow manifolds \n\u003cbr\u003e 12.10 Initialization \n\u003cbr\u003e 12.11 The method of multiple scales (Baer-Tribbia) \n\u003cbr\u003e 12.12 Nonlinear Galerkin methods \n\u003cbr\u003e 12.13 Weaknesses of the nonlinear Galerkin method \n\u003cbr\u003e 12.14 Tracking the slow manifold \n\u003cbr\u003e 12.15 Three parts to multiple scale algorithms \n\u003cbr\u003e13. Splitting \u0026amp; its cousins \n\u003cbr\u003e 13.1 Introduction \n\u003cbr\u003e 13.2 Fractional steps for diffusion \n\u003cbr\u003e 13.3 Pitfalls in splitting, I: boundary conditions \n\u003cbr\u003e 13.4 Pitfalls in splitting, II: consistency \n\u003cbr\u003e 13.5 Operator theory of time-stepping \n\u003cbr\u003e 13.6 High order splitting \n\u003cbr\u003e 13.7 Splitting and fluid mechanics \n\u003cbr\u003e14. Semi-Lagrangian advection \n\u003cbr\u003e 14.1 Concept of an integrating factor \n\u003cbr\u003e 14.2 Misuse of integrating factor methods \n\u003cbr\u003e 14.3 Semi-Lagrangian advection: introduction \n\u003cbr\u003e 14.4 Advection \u0026amp; method of characteristics \n\u003cbr\u003e 14.5 Three-level, 2D order semi-implicit \n\u003cbr\u003e 14.6 Multiply-upstream SL \n\u003cbr\u003e 14.7 Numerical illustrations \u0026amp; superconvergence \n\u003cbr\u003e 14.8 Two-level SL\/SI algorithms \n\u003cbr\u003e 14.9 Noninterpolating SL \u0026amp; numerical diffusion \n\u003cbr\u003e 14.10 Off-grid interpolation \n\u003cbr\u003e 14.10.1 Off-grid interpolation: generalities \n\u003cbr\u003e 14.10.2 Spectral off-grid \n\u003cbr\u003e 14.10.3 Low-order polynomial interpolation \n\u003cbr\u003e 14.10.4 McGregor's Taylor series scheme \n\u003cbr\u003e 14.11 Higher order SL methods \n\u003cbr\u003e 14.12 History and relationships to other methods \n\u003cbr\u003e 14.13 Summary \n\u003cbr\u003e15. Matrix-solving methods \n\u003cbr\u003e 15.1 Introduction \n\u003cbr\u003e 15.2 Stationary one-step iterations \n\u003cbr\u003e 15.3 Preconditioning: finite difference \n\u003cbr\u003e 15.4 Computing iterates: FFT\/matrix multiplication \n\u003cbr\u003e 15.5 Alternative preconditioners \n\u003cbr\u003e 15.6 Raising the order through preconditioning \n\u003cbr\u003e 15.7 Multigrid: an overview \n\u003cbr\u003e 15.8 MRR method \n\u003cbr\u003e 15.9 Delves-Freeman block-and-diagonal iteration \n\u003cbr\u003e 15.10 Recursions \u0026amp; formal integration: constant coefficient ODEs \n\u003cbr\u003e 15.11 Direct methods for separable PDE's \n\u003cbr\u003e 15.12 Fast interations for almost separable PDEs \n\u003cbr\u003e 15.13 Positive definite and indefinite matrices \n\u003cbr\u003e 15.14 Preconditioned Newton flow \n\u003cbr\u003e 15.15 Summary \u0026amp; proverbs \n\u003cbr\u003e16. Coordinate transformations \n\u003cbr\u003e 16.1 Introduction \n\u003cbr\u003e 16.2 Programming Chebyshev methods \n\u003cbr\u003e 16.3 Theory of 1-D transformations \n\u003cbr\u003e 16.4 Infinite and semi-infinite intervals \n\u003cbr\u003e 16.5 Maps for endpoint \u0026amp; corner singularities \n\u003cbr\u003e 16.6 Two-dimensional maps \u0026amp; corner branch points \n\u003cbr\u003e 16.7 Periodic problems \u0026amp; the Arctan\/Tan map \n\u003cbr\u003e 16.8 Adaptive methods \n\u003cbr\u003e 16.9 Almost-equispaced Kosloff\/Tal-Ezer grid \n\u003cbr\u003e17. Methods for unbounded intervals \n\u003cbr\u003e 17.1 Introduction \n\u003cbr\u003e 17.2 Domain truncation \n\u003cbr\u003e 17.2.1 Domain truncation for rapidly-decaying functions \n\u003cbr\u003e   \n\u003cbr\u003e 17.7 Rational Chebyshev functions: TB subscript n \n\u003cbr\u003e 17.8 Behavioral versus numerical boundary conditions \n\u003cbr\u003e 17.9 Strategy for slowly decaying functions \n\u003cbr\u003e 17.10 Numerical exemples: rational Chebyshev functions \n\u003cbr\u003e 17.11 Semi-infinite interval: rational Chebyshev TL subscript n \n\u003cbr\u003e 17.12 Numerical Examples: Chebyshev for semi-infinite interval \n\u003cbr\u003e 17.13 Strategy: Oscillatory, non-decaying functions \n\u003cbr\u003e 17.14 Weideman-Cloot Sinh mapping \n\u003cbr\u003e 17.15 Summary \n\u003cbr\u003e18. Spherical \u0026amp; Cylindrical geometry \n\u003cbr\u003e 18.1 Introduction \n\u003cbr\u003e 18.2 Polar, cylindrical, toroidal, spherical \n\u003cbr\u003e 18.3 Apparent singularity at the pole \n\u003cbr\u003e 18.4 Polar coordinates: parity theorem \n\u003cbr\u003e 18.5 Radial basis sets and radial grids \n\u003cbr\u003e 18.5.1 One-sided Jacobi basis for the radial coordinate \n\u003cbr\u003e 18.5.2 Boundary value \u0026amp; eigenvalue problems on a disk \n\u003cbr\u003e 18.5.3 Unbounded domains including the origin in Cylindrical coordinates \n\u003cbr\u003e 18.6 Annual domains \n\u003cbr\u003e 18.7 Spherical coordinates: an overview \n\u003cbr\u003e 18.8 The parity factoro for scalars: sphere versus torus \n\u003cbr\u003e 18.9 Parity II: Horizontal velocities \u0026amp; other vector components \n\u003cbr\u003e 18.10 The Pole problem: spherical coordinates \n\u003cbr\u003e 18.11 Spherical harmonics: introduction \n\u003cbr\u003e 18.12 Legendre transforms and other sorrows \n\u003cbr\u003e 18.12.1 FFT in longitude\/MMT in latitude \n\u003cbr\u003e 18.12.2 Substitutes and accelerators for the MMT \n\u003cbr\u003e 18.12.3 Parity and Legendre Transforms \n\u003cbr\u003e 18.12.4 Hurrah for matrix\/vector multiplication \n\u003cbr\u003e 18.12.5 Reduced grid and other tricks \n\u003cbr\u003e 18.12.6 Schuster-Dilts triangular matrix acceleration \n\u003cbr\u003e 18.12.7 Generalized FFT: multipoles and all that \n\u003cbr\u003e 18.12.8 Summary \n\u003cbr\u003e 18.13 Equiareal resolution \n\u003cbr\u003e 18.14 Spherical harmonics: limited-area models \n\u003cbr\u003e 18.15 Spherical harmonics and physics \n\u003cbr\u003e 18.16 Asymptotic approximations, I \n\u003cbr\u003e 18.17 Asymptotic approximations, II \n\u003cbr\u003e 18.18 Software: spherical harmonics \n\u003cbr\u003e 18.19 Semi-implicit: shallow water \n\u003cbr\u003e 18.20 Fronts and topography: smoothing\/filters \n\u003cbr\u003e 18.20.1 Fronts and topography \n\u003cbr\u003e 18.20.2 Mechanics of filtering \n\u003cbr\u003e 18.20.3 Spherical splines \n\u003cbr\u003e 18.20.4 Filter order \n\u003cbr\u003e 18.20.5 Filtering with spatially-variable order \n\u003cbr\u003e 18.20.6 Topographic filtering in meteorology \n\u003cbr\u003e 18.21 Resolution of spectral models \n\u003cbr\u003e 18.22 Vector harmonics \u0026amp; Hough functions \n\u003cbr\u003e 18.23 Radial\/vertical coordinate: spectral or non-spectral? \n\u003cbr\u003e 18.23.1 Basis for Axial coordinate in cylindrical coordinates \n\u003cbr\u003e 18.23.2 Axial basis in toroidal coordinates \n\u003cbr\u003e 18.23.3 Vertical\/radial basis in spherical coordinates \n\u003cbr\u003e 18.24 Stellar convection in a spherical annulus: Glatzmaier (1984) \n\u003cbr\u003e 18.25 Non-tensor grids: icosahedral, etc. \n\u003cbr\u003e 18.26 Robert basis for the sphere \n\u003cbr\u003e 18.27 Parity-modified latitudinal Fourier series \n\u003cbr\u003e 18.28 Projective filtering for latitudinal Fourier series \n\u003cbr\u003e 18.29 Spectral elements on the sphere \n\u003cbr\u003e 18.30 Spherical harmonics besieged \n\u003cbr\u003e 18.31 Elliptic and elliptic cylinder coordinates \n\u003cbr\u003e 18.32 Summary \n\u003cbr\u003e19. Special tricks \n\u003cbr\u003e 19.1 Introduction \n\u003cbr\u003e 19.2 Sideband truncation \n\u003cbr\u003e 19.3 Special basis functions, I: corner singularities \n\u003cbr\u003e 19.4 Special basis functions, II: wave scattering \n\u003cbr\u003e 19.5 Weakly nonlocal solitary waves \n\u003cbr\u003e 19.6 Root-finding by Chebyshev polynomials \n\u003cbr\u003e 19.7 Hilbert transform \n\u003cbr\u003e 19.8 Spectrally-accurate quadrature methods \n\u003cbr\u003e 19.8.1 Introduction: Gaussian and Clenshaw-Curtis quadrature \n\u003cbr\u003e 19.8.2 Clenshaw-Curtis adaptivity \n\u003cbr\u003e 19.8.3 Mechanics \n\u003cbr\u003e 19.8.4 Integration of periodic functions and the trapezoidal rule \n\u003cbr\u003e 19.8.5 Infinite intervals and the trapezoidal rule \n\u003cbr\u003e 19.8.6 Singular integrands \n\u003cbr\u003e 19.8.7 Sets and solitaries \n\u003cbr\u003e20. Symbolic calculations \n\u003cbr\u003e 20.1 Introduction \n\u003cbr\u003e 20.2 Strategy \n\u003cbr\u003e 20.3 Examples \n\u003cbr\u003e 20.4 Summary and open problems \n\u003cbr\u003e21. The Tau-method \n\u003cbr\u003e 21.1 Introduction \n\u003cbr\u003e 21.2 tau-Approximation for a rational function \n\u003cbr\u003e 21.3 Differential equations \n\u003cbr\u003e 21.4 Canonical polynomials \n\u003cbr\u003e 21.5 Nomenclature \n\u003cbr\u003e22. Domain decomposition methods \n\u003cbr\u003e 22.1 Introduction \n\u003cbr\u003e 22.2 Notation \n\u003cbr\u003e 22.3 Connecting the subdomains: patching \n\u003cbr\u003e 22.4 Weak coupling of elemental solutions \n\u003cbr\u003e 22.5 Variational principles \n\u003cbr\u003e 22.6 Choice of basis \u0026amp; grid \n\u003cbr\u003e 22.7 Patching versus variational formalism \n\u003cbr\u003e 22.8 Matrix inversion \n\u003cbr\u003e 22.9 The influence matrix method \n\u003cbr\u003e 22.10 Two-dimensional mappings \u0026amp; sectorial elements \n\u003cbr\u003e 22.11 Prospectus \n\u003cbr\u003e23. Books and reviews \n\u003cbr\u003e A. A bestiary of basis functions \n\u003cbr\u003e A.1 Trigonometric basis functions: Fourier series \n\u003cbr\u003e A.2 Chebyshev polynomials T subscript n (x) \n\u003cbr\u003e A.3 Chebyshev polynomials of the second kind: U subscript n (x) \n\u003cbr\u003e A.4 Legendre polynomials: P subscript n (x) \n\u003cbr\u003e A.5 Gegenbauer polynomials \n\u003cbr\u003e A.6 Hermite polynomials: H subscript n (x) \n\u003cbr\u003e A.7 Rational Chebyshev functions: TB subscript n (y) \n\u003cbr\u003e A.8 Laguerre polynomials: L subscript n (x) \n\u003cbr\u003e A.9 Rational Chebyshev functions: TL subscript n (y) \n\u003cbr\u003e A.10 Graphs of convergence domains in the complex plane \n\u003cbr\u003e B. Direct matrix-solvers \n\u003cbr\u003e B.1 Matrix factorizations \n\u003cbr\u003e B.2 Banded matrix \n\u003cbr\u003e B.3 Matrix-of-matrices theorem \n\u003cbr\u003e B.4 Block-banded elimination: the \"Lindzen-Kuo\" algorithm \n\u003cbr\u003e B.5 Block and \"bordered\" matrices \n\u003cbr\u003e B.6 Cyclic banded matrices (periodic boundary conditions) \n\u003cbr\u003e B.7 Parting shots \n\u003cbr\u003e C. Newton iteration \n\u003cbr\u003e C.1 Introduction \n\u003cbr\u003e C.2 Examples \n\u003cbr\u003e C.3 Eigenvalue problems \n\u003cbr\u003e C.4 Summary \n\u003cbr\u003e D. The continuation method \n\u003cbr\u003e D.1 Introduction \n\u003cbr\u003e D.2 Examples \n\u003cbr\u003e D.3 Initialization strategies \n\u003cbr\u003e D.4 Limit Points \n\u003cbr\u003e D.5 Bifurcation points \n\u003cbr\u003e D.6 Pseudoarclength continuation \n\u003cbr\u003e E. Change-of-Coordinate derivative transformations \n\u003cbr\u003e F. Cardinal functions \n\u003cbr\u003e F.1 Introduction \n\u003cbr\u003e F.2 General Fourier series: endpoint grid \n\u003cbr\u003e F.3 Fourier Cosine series: endpoint grid \n\u003cbr\u003e F.4 Fourier Sine series: endpoint grid \n\u003cbr\u003e F.5 Cosine cardinal functions: interior grid \n\u003cbr\u003e F.6 Sine cardinal functions: interior grid \n\u003cbr\u003e F.7 Sinc(x): Whittaker cardinal function \n\u003cbr\u003e F.8 Chebyshev Gauss-Lobatto (\"endpoints\") \n\u003cbr\u003e F.9 Chebyshev polynomials: interior or \"roots\" grid \n\u003cbr\u003e F.10 Legendre polynomials: Gauss-Lobatto grid \n\u003cbr\u003e G. Transformation of derivative boundary conditions \n\u003cbr\u003e Glossary; Index; References\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003eMarc Notes\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tIncludes bibliographical references (p. 595-668) and index.\u003cbr\u003e\u003cbr\u003e\n\u003c\/p\u003e\n\u003cbr\u003e\n\u003cbr\u003e\n\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n","brand":"Dover Publications","offers":[{"title":"Default Title","offer_id":46431146606723,"sku":"SPTM-9780486411835","price":37.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0564\/6830\/8099\/files\/9780486411835_spiral.png?v=1769660253","url":"https:\/\/sebink.com\/products\/chebyshev-and-fourier-spectral-methods-revised","provider":"Sebink","version":"1.0","type":"link"}