DIRECT SOLUTION OF THE DYNAMICAL ELASTICITY PROBLEM FOR A QUARTER SPACE
Bibliographic record
Abstract
The wave field of an elastic quarter space is constructed when one face is rigidly fixed and a dynamic normal compressive load is concentrated at the point on another face. The problem was solved by the direct application of the integral Laplace and Fourier transforms to the motion equations and the boundary conditions. This operation leads to the one-dimensional vector inhomogeneous boundary value problem with respect to unknown displacement’s transformants. The problem was solved using the matrix differential calculus. A fundamental matrix and a decreasing solution to the corresponding homogenous matrix equation were constructed with a basic residue theorem. A singular integral equation was obtained in the process by satisfying unrealized boundary condition. Weakly convergent part of the equation was summed up. The behavior of the unknown function had been analyzed based on its mechanical sense. The form of unknown function was expressed as a series on Laguerre polynomials. The original displacements’ field was found after an application the inverse integral transforms.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".