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Tensors and Hypermatrices
Lek-Heng Lim University of Chicago 15.1 Hypermatrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-2 15.2 Tensors and Multilinear Functionals. . . . . . . . . . . . . . . . . 15-6 15.3 Tensor Rank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-12 15.4 Border Rank . . . . . . . . . . . . . . . . . . . . . . . ....
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1. Simplices, ∆-Complexes, and Homology: 1/8/15 1 2. Properties of Singular Homology: 1/13/15 4 3. Homotopy Invariance of Singular Homology: 1/15/15 7 4. Applications of Homotopy Invariance and Excision: 1/20/15 10 5. Equivalence of Singular and Simplicial Homology: 1/22/15 14 6. Degrees of Maps on Sn: 1/27/15 17 7. The Mayer-Vietoris Sequence and Applications: 1/29/15 20 8. CW Complexes: 2/3/1...
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1. Outer Measure and the Lesbegue Measure: 8/26/15 1 2. Defining the Lesbegue Measure: 8/31/15 3 3. Measurable Functions: 9/2/15 6 4. Semicontinuous Functions and Review: 9/4/15 8 5. Some More Review and the Convergence Theorems: 9/9/15 9 6. Completeness of the Space of Integrable Functions: 9/11/15 11 7. Fubini’s Theorem and Differentiability: 9/14/15 12 8. The Vitali Covering Lemma: 9/16/15 1...
متن کاملSimple approach for the preparation of 15−15N2-enriched water for nitrogen fixation assessments: evaluation, application and recommendations
Recent findings revealed that the commonly used (15)N2 tracer assay for the determination of dinitrogen (N2) fixation can underestimate the activity of aquatic N2-fixing organisms. Therefore, a modification to the method using pre-prepared (15-15)N2-enriched water was proposed. Here, we present a rigorous assessment and outline a simple procedure for the preparation of (15-15)N2-enriched water....
متن کاملMatrix Perturbation Theory
Ren-Cang Li University of Texas at Arlington 15.1 Eigenvalue Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-1 15.2 Singular Value Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-6 15.3 Polar Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-7 15.4 Generalized Eigenvalue Problems . . . . . . . . . . . . . . . . . . . 15-...
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