On Solvability of an Inverse Boundary Value Problem for Pseudo Hyperbolic Equation of the Fourth Order
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Bibliographic record
Abstract
We analyze the solvability of the inverse boundary problem with an unknown coefficient depended on time for the pseudo hyperbolic equation of fourth order with periodic and integral conditions.The initial problem is reduced to an equivalent problem. With the help of the Fourier method, the equivalent problem is reduced to a system of integral equations. The existence and uniqueness of the solution of the integral equations is proved. The obtained solution of the integral equations is also the only solution to the equivalent problem. Basing on the equivalence of the problems, the theorem of the existence and uniqueness of the classical solutions of the original problem is proved.
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Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.022 | 0.032 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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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