[ARTICLE] Applied Physics of Extended (or Gamma) Sine and Cosine Functions (Canadian Journal of Applied Physics Research / 2023)
Bibliographic record
Abstract
Evolution of fundamental mathematical tools (such as trigonometric functions sin(α) and cos(α)) has inherent repercusions on how we solve problems in applied physics. Recently published (see links below) extended or gamma sine function sin∗(α, γ) and cosine function cos∗(α, γ) — along with their upgraded identity angle sum and subtraction rules sin∗(A ± B, γ) and cos∗(A ± B, γ) — have enabled a new approach on how to tackle practical problems using mathematics (a published example is the energy-coupled mass-spring oscilatory system). The usefullness of a theory is measured by both the insight it generates, and the solution it produces, when applied to physical problems with pertinent applications. Its acceptance amongst peers depends on the availability of such examples, as way-showers of how the theory can be applied in practice, and how useful results can be derived by employing it in similar or related examples/problems. This article has the purpose of providing this bridge between the above theories and its application in some common scientific fields. Several exercises are solved employing these new formulae, and new potential applications are identified that cover various topics in physics such as civil engineering (i.e., measuring distances in bridges), aerospace and aeronautics (i.e., turbine velocity triangles and optimum orbital deployment for a satellite constellation) and telecommunications (i.e., antenna array beamforming and steering, as well as new modulations based on quadrature phase-shift keying). These problems (and solutions) are designed to indicate the usefullness of these new expanded functions, and can become practical classroom exercises applicable to both academic and professional environments.APR link: Applied Physics of Extended (or Gamma) Sine and Cosine FunctionsJMR link #1: Extended Angle Sum and Difference Identity Rules for Scalene TrianglesJMR link #2: Extended Sine and Cosine Functions for Scalene Triangles<b>Copyrights</b>Copyright for this article is retained by the author(s), with first publication rights granted to the journal. This is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).-------------------------------------------------------------------------For more public data, please visit my Figshare profile: https://figshare.com/authors/Luis_Teia/10811244
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 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) | 0.011 | 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 teacher head, 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".