Manuscript XVI-M@1 · XVI-M.tex · section · 7346c909
Scale derivative versus dilation defect at every grade (work package B)
M.6 Dilation identity, residues, and matched scale variation › Scale derivative versus dilation defect at every grade (work package B) · lines 1756–1778
of the full scale tensor. for all . Collapse and adjoint defect are homogeneous in the total derivative degree , so the top part () and the lower parts () cannot cancel each other; cross-grade cancellations at fixed are included.
| reading | nnz () | adjoint-defect nnz | variational | per- nnz () |
|---|---|---|---|---|
| formal | 14112 | 16608 | no | 744, 4440, 10278, 10040, 4604 |
| -plateau | 2522 | 4090 | no | 744, 1728, 2386, 1550, 514 |
| preparation plateau | 4580 | 4090 | no | 0, 0, 2274, 4072, 4604 |
| double plateau | 490 | 0 | yes | 0, 0, 474, 514, 514 |
Lower-order envelope (all ): is injective on each -block; self-adjoint parameter subspaces have dimensions () in the formal, - and preparation readings and in the double plateau; there image () and image is one-dimensional (). The radial specialization is non-self-adjoint at and in every reading. Time-only readings: Corollary cor:wpB-timeonly.
Nearby in this section
- scope: Status (work package B).
- section: Scale derivative versus dilation defect at every grade (work package B)
- lemma: Lemma: Complete scale derivative of the subtraction functions
- theorem: Theorem: Scale derivative equals dilation defect at every grade
- section: Scale derivative versus dilation defect at every grade (work package B)
- theorem: Theorem: Double-plateau scale tensor: top component and full tensor
- proposition: Proposition: Exact separating functional for the displayed scale functional (audit 3)
- remark: Remark: Top contact versus full tensor; relation to XVI-L