Results 51 to 60 of about 104 (81)
We establish rigorous mathematical boundaries for self-referential systems and prove that stable self-reference exists if and only if the self-reference parameter lies within the interval $[e^{-e}, e^{1/e}] \approx [0.0659, 1.4446]$. This "tetration bound" provides fundamental limits for recursive intelligence, consciousness, and complex adaptive ...
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Advances in Computational Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
William Paulsen
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Skolem + Tetration Is Well-Ordered
Lecture Notes in Computer Science, 2009 The problem of whether a certain set of number-theoretic functions --- defined via tetration (i.e. iterated exponentiation) --- is well-ordered by the majorisation relation , was posed by Skolem in 1956. We prove here that indeed it is a computable well-order , and give a lower bound *** 0 on its ordinal.
Mathias Barra, Philipp Gerhardy
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The Ordinal of Skolem + Tetration Is τ 0
Lecture Notes in Computer Science, 2010 In [1], we proved that a certain family of number theoretic functions S* is well-ordered by the majorisation relation '≤'. Furthermore, we proved that a lower bound on the ordinal O(S*, ≤) of this well-order is the least critical epsilon number τ 0. In this paper we prove that τ0 is also an upper bound for its ordinal, whence our sought-after result, O(
Mathias Barra, Philipp Gerhardy
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Signal Reconstruction using Second Order Tetration Polynomial
2019 34th International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC), 2019 In this paper, we propose the novel method for signal reconstruction based on the tetration polynomial. The second order tetration polynomial is applied to construct the interpolation formulae. However, this polynomial has a shift-variant and asymmetric properties. These properties are used to build several formulae which have specific characteristics.
Suphongsa Khetkeeree
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Applied Stochastic Models in Business and Industry, 2020 AbstractA 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, Pareto, and Gompertz distributions.
Yann Dijoux
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Tetration: Iterative Enjoyment
College Mathematics Journal, 2022Abe Edwards, Brielle Komosinski
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Distributions Derived from the Continuous Iteration of the Hyperbolic Sine Function
Mathematical Methods of Statistics, 2023 International audienceFamilies of distributions built from the fractional or continuous iteration of exponential-type functions are characterized by a wide range of tail-heaviness.
Yann Dijoux
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Topological Order in an Antiferromagnetic Tetratic Phase
Physical Review Letters, 2022We study lattice melting in two-dimensional systems of spinful particles that interact antiferromagnetically. We argue that, for strong spin interactions, single lattice dislocations are forbidden by magnetic frustration. This leads to a melting scenario in which a tetratic phase, containing free dislocation pairs and bound disclinations, separates the
Daniel Abutbul, Daniel Podolsky
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Self‐Assembled Tetratic Crystals by Orthogonal Colloidal Force
Small, 2023AbstractBonding simple building blocks to create crystalline materials with design has been sophisticated in the molecular world, but this is still very challenging for anisotropic nanoparticles or colloids, because the particle arrangements, including position and orientation, cannot be manipulated as expected. Here biconcave polystyrene (PS) discs to
Shanshan Li +4 more
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