Bibliographic record
Abstract
Our aim in this paper is to expose the interesting role played by differ integral (specifically, semi derivatives and semi integrals)in solving certain diffusion problems.Along with the wave equation and Laplace equation, the diffusion equation is one of the three fundamental partial differential equation of mathematical physics.I will not discuss convential solutions of the diffusion equation at all.These range from closed form solutions for very simple model problems to computer methods for approximating concentration of the diffusing substance on a network of points.Such solutions are described extensively in the literature .My purpose, rather, is to expose a technique for partially solving a family of diffusion problems, a technique that leads to a equation which is first order partially and half order temporally.I shall show that, for semi finite systems initially at equilibrium, our semi differential equation leads to a relationship between the intensive variable and the flux at the boundary.Use of this relationship then obviates the need to solve the original diffusion equation in those problems for which this behavior at the boundary is of primary importance.I shall, in fact, freely make use of the general properties established for differ integral operators as if all my functions were differ integrable.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".