Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi Polynomials
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Bibliographic record
Abstract
In the present paper, we numerically simulate fractional-order model of the Bloch equation by using the Jacobi polynomials. It arises in chemistry, physics and nuclear magnetic resonance (NMR). It also arises in magnetic resonance imaging (MRI) and electron spin resonance (ESR). It is used for purity determination, provided that the molecular weight and structure of the compound is known. It can also be used for structural determination. By the study of NMR, chemists can determine the structure of many compounds. The obtained numerical results are compared and simulated with the known solutions. Accuracy of the proposed method is shown by providing tables for absolute errors and root mean square errors. Different orders of the time-fractional derivatives results are illustrated by using figures.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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