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
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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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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it