Deformed mathematical objects stemming from the $q$-logarithm function
| Autor: | Borges, Ernesto P., da Costa, Bruno G. |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | Generalized numbers, arithmetic operators and derivative operators, grouped in four classes based on symmetry features, are introduced. Their building element is the pair of $q$-logarithm/$q$-exponential inverse functions. Some of the objects were previously described in the literature, while others are newly defined. Commutativity, associativity and distributivity, and also a pair of linear/nonlinear derivatives are observed within each class. Two entropic functionals emerge from the formalism, one of them is the nonadditive Tsallis entropy. Comment: 33 pages, 4 figures (14 eps files) |
| Databáze: | arXiv |
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