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Composition Operations of Generalized Entropies Applied to the Study of Numbers

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  • Amelia Carolina Sparavigna

Abstract

The generalized entropies of C. Tsallis and G. Kaniadakis have composition operations, which can be applied to the study of numbers. Here we will discuss these composition rules and use them to study some famous sequences of numbers (Mersenne, Fermat, Cullen, Woodall and Thabit numbers). We will also consider the sequence of the repunits, which can be seen as a specific case of q-integers.

Suggested Citation

  • Amelia Carolina Sparavigna, 2019. "Composition Operations of Generalized Entropies Applied to the Study of Numbers," International Journal of Sciences, Office ijSciences, vol. 8(04), pages 87-92, April.
    • Handle: RePEc:adm:journl:v:8:y:2019:i:4:p:87-92
    DOI: 10.18483/ijSci.2044
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    References listed on IDEAS

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    1. Amelia Carolina Sparavigna, 2015. "Gray-Level Image Transitions Driven by Tsallis Entropic Index," International Journal of Sciences, Office ijSciences, vol. 4(02), pages 16-25, February.
    2. Amelia Carolina Sparavigna, 2015. "Shannon, Tsallis And Kaniadakis Entropies In Bi-level Image Thresholding," International Journal of Sciences, Office ijSciences, vol. 4(02), pages 35-43, February.
    3. Amelia Carolina Sparavigna, 2015. "Relations Between Tsallis and Kaniadakis Entropic Measures and Rigorous Discussion of Conditional Kaniadakis Entropy," International Journal of Sciences, Office ijSciences, vol. 4(10), pages 47-50, October.
    4. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    5. Amelia Carolina Sparavigna, 2015. "On The Generalized Additivity Of Kaniadakis Entropy," International Journal of Sciences, Office ijSciences, vol. 4(02), pages 44-48, February.
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    Cited by:

    1. Amelia Carolina Sparavigna, 2019. "Some Groupoids and their Representations by Means of Integer Sequences," International Journal of Sciences, Office ijSciences, vol. 8(10), pages 1-5, October.

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