Bibliographic record
Abstract
This doctoral dissertation consists of three refereed open access papers. These papers comprise chapters 2-4 herein. They deal with problems arising from a study of various differential equations with indefinite principal parts whether they be classified as ordinary, abstract, or fractional. In the first paper (Chapter 2) we show that Sturm's separation theorem always fails for a classical real two term second order differential equation in the event that the principal part has one turning point inside the interval of definition. In the second paper (Chapter 3) we consider differential equations defined by so-called conformable derivatives and show that these differential operators are essentially multiplication operators (by a possibly sign-indefinite leading term) on a space of ordinary derivatives of functions. In the third paper (Chapter 4) we prove existence and uniqueness theorems for initial value problems and two-point boundary problems associated with fractional differential equations defined by composition of right Caputo differential operators and left Riemann-Liouville differential operators with indefinite principal parts.
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How this classification was reachedexpand
Full frame distilled prediction
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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; both teacher heads agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".