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| Autori principali: | , |
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| Natura: | Recurso digital |
| Lingua: | |
| Pubblicazione: |
Zenodo
2025
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| Accesso online: | https://doi.org/10.5281/zenodo.17848505 |
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Sommario:
- <p>In this paper, we investigate the role of commutative Bennett operations (commutative<br>hyperoperations) in Min-Plus and Max-Plus algebras, and in the dequantization of classical<br>polynomials into tropical polynomials. We reformulate the dequantization process using<br>commutative Bennett operations, yielding a framework that suggests potential alternatives<br>to Maslov dequantization. The formal development of these alternatives is left as an open<br>problem.<br>We apply these commutative Bennett operations to derive generalized forms of the raw<br>and central moments, emphasizing the value of studying these moments collectively rather<br>than in isolation. This motivates the introduction of structural constraints on the family of<br>resulting coefficients, along with interpretations for such structure.<br>The paper further proposes an iterative method for fitting probability density func-<br>tions to empirical data, including the use of a simple kernel K(x)=x. Additional statis-<br>tical constructions-such as generalized inner products, covariance, and Pearson’s correlation<br>coefficient-are reexpressed through commutative Bennett operations.<br>Finally, we introduce two approaches for defining commutative Bennett operations be-<br>tween matrices: one by equipping each matrix with a compatible algebra and transferring<br>the operations to these derived structures, and another derived directly from our generalized<br>inner product.</p>