Weyl transforms and a degenerate elliptic partial differential equation
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Bibliographic record
Abstract
We give a formula for the inverse of a degenerate elliptic partial differential operator P on related to the Heisenberg group. The formula is in terms of pseudo-differential operators of the Weyl type, i.e. Weyl transforms. The technique is to use the Fourier–Wigner transforms of Hermite functions, which form an orthonormal basis for . Using the formula for the inverse, we give an estimate for the L p norm of the solution u of the partial differential equation Pu = f on in terms of the L 2 norm of f , 2≤ p ≤∞.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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