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. PrefaceThis integrated thesis consists of four chapters: Chapter 1 consists of an introduction to the questions and the problems considered in the thesis.Chapters 2-4 consist of complete reprints of published papers.Note that all articles are reproduced in whole as they appeared in open access journals.The thesis supervisor (ABM) attests that the student was fully involved in setting up and conducting the research, obtaining the data and analyzing all the results, as well as preparing and writing the material presented in the three attached jointly co-authored article(s) integrated within this thesis.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
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; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
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".