Description of a program for Computing eigenvalues and eigenfunctions and their first derivatives with respect to the parameter of the coupled parametric self-adjoined elliptic differential equations
Bibliographic record
Abstract
IBM Toronto Lab,8200 Warden Avenue, Markham, ON L6G 1C7, CanadaBrief description of a FORTRAN 77 program is presented for calculating with the givenaccuracy eigenvalues, eigenfunctions and their first derivatives with respect to the parameterof the coupled parametric self-adjoined elliptic differential equations with the Dirichlet and/orNeumann type boundary conditions on the finite interval. The original problem is projectedto the parametric homogeneous and nonhomogeneous 1D boundary-value problems for a set ofordinary second order differential equations which is solved by the finite element method. Theprogram calculates also potential matrix elements – integrals of the eigenfunctions multipliedby their first derivatives with respect to the parameter. Parametric eigenvalues (so-calledpotential curves) and matrix elements computed by the POTHEA program can be used forsolving the bound state and multi-channel scattering problems for a system of the coupledsecond-order ordinary differential equations with the help of the KANTBP programs. Asa test desk, the program is applied to the calculation of the potential curves and matrixelements of Schr¨odinger equation for a system of three charged particles with zero totalangular momentum.Key words and phrases: boundary value problem, finite element method, Kantorovichmethod.
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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) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.063 | 0.025 |
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".