On the stability of second order parametric ordinary differential equations and applications
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Bibliographic record
Abstract
This paper investigates the Lipschitz stability for a parametric version of the general second order Ordinary Differential Equation (ODE) initial-value Cauchy problem.Based on a direct computation using Perov's inequality, we first establish a Lipschitz stability result for this problem under a partial variation of the data.Next, we apply our abstract result to second order differential equations governed by cocoercive operators.Then, we discuss more concrete applications of the stability for two specific applied mathematical models inherent in electricity and control theory.Finally, we provide numerical tests based on the software source Scilab, which are done with respect to parametric linear time invariant systems, illustrating the validity of our theoretical results.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.003 |
| 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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