Geodesic
Generalization and unification of the concepts of remainder of division and fractional part, maximization of entropy of fractional part of convolution with uniform distribution
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2022), pp. 45-52 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article considers the issue of preserving the information property of convolution with canonical uniform distribution in the cases of arbitrary finite lattice and arbitrary segment. For this purpose, the generalization and the unification of the concepts of remainder of division and fractional part are proposed.
Mots-clés : convolution, fractional part
Keywords: uniform distribution, entropy. 
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     author = {A. E. Kondratenko and V. N. Sobolev},
     title = {Generalization and unification of the concepts of remainder of division and fractional part, maximization of entropy of fractional part of convolution with uniform distribution},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {45--52},
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A. E. Kondratenko; V. N. Sobolev. Generalization and unification of the concepts of remainder of division and fractional part, maximization of entropy of fractional part of convolution with uniform distribution. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2022), pp. 45-52. http://geodesic.mathdoc.fr/item/VTPMK_2022_1_a3/

[1] Condratenko A. E., Sobolev V. N., “On the information property of convolution with uniform distribution: Fundamental and applied problems of mathematics and Computer science”, Materials of the XIV International Conference, DSU Publishing House, Makhachkala, 2021, 135–138 (in Russian)

[2] Chechyota S. I., Vvedenie v diskretnuyu teoriyu informatsii i kodirovaniya, MTsMNO, Moscow, 2011, 224 pp. (in Russian)

[3] Condratenko A. E., Sobolev V. N., “On the Entropy Maximization in Convolution with Uniform Distribution”, Herald of Dagestan State University, 37:1 (2022), 7–11 (in Russian) | DOI