THE PROBLEM OF NEW PROPERTIES OF NUMBERS

Autor: L.G. Sushkov

Publikováno v: Надежность и качество сложных систем, Iss 2 (2024)

Background. The proposed work is devoted to research to clarify the axiomatization of arithmetic in connection with the presence of special assumptions in it. The conceptual problem of analyzing new properties of numbers is formulated under the ass

Externí odkaz: https://doaj.org/article/c7c91049168c4bffb88e15278813d5c0

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A new class of distributions on the whole real line based on the continuous iteration approach

Autor: Yann Dijoux

Publikováno v: Communications in Statistics - Theory and Methods. 52:4934-4959

The continuous iteration of an exponential-type function allows to describe a whole range of growths between logarithmical and exponential. This principle has been applied to a class of lifetime di...

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::59031267bebcd7a312f61402a848f724
https://doi.org/10.1080/03610926.2021.1991376

A Reduction of Integer Factorization to Modular Tetration

Autor: Markus Hittmeir

Publikováno v: International Journal of Foundations of Computer Science. 31:461-481

Let $a,k\in\mathbb{N}$. For the $k-1$-th iterate of the exponential function $x\mapsto a^x$, also known as tetration, we write \[ ^k a:=a^{a^{.^{.^{.^{a}}}}}. \] In this paper, we show how an efficient algorithm for tetration modulo natural numbers $

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fd5f77ea8663f2e7fbe1e174e9de3f48
https://doi.org/10.1142/s0129054120500197

Construction of the tetration distribution based on the continuous iteration of the exponential‐minus‐one function

Autor: Yann Dijoux

Publikováno v: Applied Stochastic Models in Business and Industry
Applied Stochastic Models in Business and Industry, Wiley, In press, ⟨10.1002/asmb.2538⟩
Applied Stochastic Models in Business and Industry, 2020, 36 (5), pp.891-916. ⟨10.1002/asmb.2538⟩

International audience; A new class of lifetime distributions, called tetration distribution, is presented based on the continuous iteration of the exponential-minus-one function. In particular, this distribution encompasses and extends the Weibull,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::28afba26be1f65a1a406799a7252c578
https://hal-utt.archives-ouvertes.fr/hal-02560102