Determination of singularities of a function from its perturbation expansion
Bibliographic record
Abstract
The method for the determination of the position of the pair of complex conjugate branch points suggested in previous studies is generalized here. The method is modified in order to consider cases where the value of the function at the singularity is not real. A method is proposed for the determination of single isolated singularities located either on the real axis or in the complex plane. These methods are applied to three eigenvalue problems, namely the bounded delta-potential atom, the Mathieu equation and the hydrogen atom in a spherically symmetric cavity. We show that the position of the singularities can be obtained very accurately with minimal number of perturbation coefficients. If we take the characteristic polynomial for variational energy levels as an approximate implicit equation, the method can be used for the investigation of the analytic structure of the energy considered as a function of complex coupling constant. In particular, we show that the first singularity appears at the point of intersection of the ground and the first excited states. The second singularity, when the first and second excited states intersect, can be determined either from the expansion at the first singularity or from the expansion of the second excited state at the origin.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".