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| Matrices: Definitions and Fundamental Operations | |
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| Fundamental Matrix Operations | |
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| Linear Algebra | |
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| Eigenvalues | |
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| Linear Transformations | |
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| Rotation of Axes | |
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| The Metric Tensor | |
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| Symmetry of Finite Objects | |
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| Groups | |
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| Representations | |
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| Point Groups | |
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| Basis Functions | |
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| Symmetry of Infinitely Repeated Patterns | |
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| Bravais Lattices | |
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| Space Groups | |
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| Vectors | |
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| Scalar and Vector Products | |
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| The Reciprocal Lattice | |
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| The Orientation Matrix | |
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| Zones and Forms | |
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| Sublattices and Superlattices | |
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| Tensors | |
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| Covariance and Contravariance | |
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| The Multivariate Normal Disribution | |
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| Anisotropic Atomic Displacement Factors | |
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| The Equivalent Isotropic Temperature Factor | |
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| Effect of Symmetry | |
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| Tensors of Higher Ranks | |
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| Moments and Cumulants | |
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| Rigid Body Motion | |
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| Data Fitting | |
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| Fitting Functions | |
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| Finding the Minimum | |
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| False Minima | |
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| Estimation of Uncertainty | |
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| Estimates | |
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| The Precision of Estimates of Precision | |
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| Models with More than One Parameter | |
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| Estimates of Precision When the Model Is Not Least Squares | |
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| Significance and Accuracy | |
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| The F Distribution | |
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| Student's t Distribution | |
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| Correlation | |
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| Relationship Between Precision and Accuracy | |
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| Uncertainties of Derived Functions | |
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| The Projection Matrix | |
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| Constrained Crystal Structure Refinement | |
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| The Observed Data | |
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| The Model | |
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| The General Form for a Constrained Model | |
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| Shape Constraints | |
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| Rigid Body Thermal Motion Constraints | |
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| Chemical Constraints | |
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| Representing non-Gaussian Distributions | |
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| The Fast Fourier Transform | |
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| The Discrete Fourier Transform | |
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| The Good-Thomas Algorithm | |
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| The Cooley-Tukey Algorithm | |
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| Prime Numbers | |
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| FFTs for Real Sequences | |
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| Space Group Symmetry | |
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| Stereographic Projection | |
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| Eigenvalues and Eigenvectors of 3 x 3 Symmetric Matrices | |
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| Sublattices and Superlattices | |
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| The Probability Integral, the Gamma Function, and Related Topics | |
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| The Harmonic Oscillator in Quantum Mechanics: Bloch's Theorem | |
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| Symmetry Restrictions on Second, Third, and Fourth Rank Tensors | |
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| Some Useful Computer Programs | |
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| Bibliography | |
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| Index | |