Sturm theorems and distance between adjacent zeros for second order integro-differential equations
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Bibliographic record
Abstract
Between two adjacent zeros of any nontrivial solution of the second order ordinary differential equation x (t) + a(t)x (t) + b(t)x(t) = 0 there is one and only one zero of every nonproportional solution. This principle of zeros' distribution is known as the Sturm separation theorem which is a basis of many classical results on oscillation and asymptotic properties and on boundary value problems for ordinary differential equations. For delay and integro-differential equations this principle of zeros' distribution is not true. In this paper, the assertion on validity of the Sturm separation theorem are proposed. Distance between two zeros of nontrivial solutions to integro-differential equations is estimated.
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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.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 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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