Results 31 to 40 of about 104 (81)
The Limits of a Family; of Asymptotic Solutions to The Tetration Equation
, 2021 In this paper we construct a family of holomorphic functions $β_λ(s)$ which are solutions to the asymptotic tetration equation. Each $β_λ$ satisfies the functional relationship ${\displaystyle β_λ(s+1) = \frac{e^{β_λ(s)}}{e^{-λs} + 1}}$; which asymptotically converges as $\log β_λ(s+1) = β_λ(s) + \mathcal{O}(e^{-λs})$ as $\Re(λs) \to \infty$.
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Tetration: an iterative approach
, 2014 A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order approximations suggest that tetration may come to be of great interest for the description of involved dynamical ...
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A Few Interactions Improve Distributed Nonparametric Estimation, Optimally
, 2023 Consider the problem of nonparametric estimation of an unknown $\beta$-H\"older smooth density $p_{XY}$ at a given point, where $X$ and $Y$ are both $d$ dimensional.
Liu, Jingbo
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In pursuit of the tetratic phase in hard rectangles
Physical Review ResearchWe numerically investigate two-dimensional systems of hard rectangles at constant pressure through extensive hard-particle Monte Carlo simulations. We determine the complete phase diagram as a function of packing fraction and aspect ratio, which consists of four distinct phases.
Denis Dertli, Thomas Speck
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Mixing Estimates for Passive Scalar Transport by $BV$ Vector Fields
We prove a quantitative mixing estimate for the Cauchy problem for transport along divergence-free vector fields with bounded variation. By developing a framework that quantifies Ambrosio's regularisation scheme, we derive the first explicit bounds on ...
Huysmans, Lucas, Said, Ayman Rimah
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Mesoporous Silica Nanoparticles: Types, Synthesis, Role in the Treatment of Alzheimer's Disease, and Other Applications. [PDF]
Pharmaceutics, 2023 Sivamaruthi BS +6 more
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On the last digits of tetrations of base $2^{k}$ and $5^{k}$
, 2021 In this paper will be proved the existence of a formula to reduce a tetration of base $2^{k}$ and $5^{k}$ $\mod 10^{n}$. Indeed, last digits of a tetration are the same starting from a certain hyper-exponent; In order to compute the last digits of those expressions we reduce them $\mod 10^{n}$.
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Observations regarding the repetition of the last digits of a tetration of generic base
, 2021 9 pages, 6 tables, v3: minor edits and different form of the ...
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The Last Digits of Infinity (On Tetrations Under Modular Rings)
, 2019 A tetration is defined as repeated exponentiation. As an example, 2 tetrated 4 times is 2^(2^(2^2)) = 2^16. Tetrated numbers grow rapidly; however, we will see that when tetrating where computations are performed mod n for some positive integer n, there ...
Stowe, William
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Balanced Technical Computing - Solving Big Data problems a novel way
, 2015 Laplace’s explanation of the special 4:2:1 orbit ratio of Jupiter’s 3 innermost Galilean moons, the “Laplace resonance”, was assumed by Astronomers for centuries to be a stable phenomenon.
Raeber, Rene, Noll, Landon
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