Results 1 to 10 of about 3,402 (148)
A simple proof of generalizations of number-theoretic sums [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2022 For positive integers 𝑘, 𝑚, and 𝑛, let 𝑆𝑘 𝑚(𝑛) be the sum of all elements in the finite set {𝑥 𝑘 : 1 ≤ 𝑥 ≤ 𝑛⁄𝑚 , (𝑥, 𝑛) = 1}. The formula for 𝑆𝑘 𝑚(𝑛) is established and simpler formulae for 𝑆𝑘 𝑚(𝑛) under some conditions on 𝑚 and 𝑛 are verified. The
Yanapat Tongron +1 more
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Quotients of arithmetical functions under the Dirichlet convolution [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 We study existence of a solution of the arithmetical equation f*h = g in f, where f*h is the Dirichlet convolution of arithmetical functions f and h, and derive an explicit expression for the solution. As applications we obtain expressions for the Möbius
Pentti Haukkanen
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A Formula for the Möbius Function of the Permutation Poset Based on a Topological Decomposition [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The poset P of all permutations ordered by pattern containment is a fundamental object of study in the field of permutation patterns. This poset has a very rich and complex topology and an understanding of its Möbius function has proved particularly ...
Jason P Smith
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The structure of extended function groups
Cubo, 2021 Conformal (respectively, anticonformal) automorphisms of the Riemann sphere are provided by the Möbius (respectively, extended Möbius) transformations.
Rubén A. Hidalgo
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Two generalizations of Liouville λ function [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 We study the properties of two classes of functions λₖ and ~λₖ that generalize the Liouville λ function, including some equivalencies between the Riemann hypothesis and some assertions about the asymptotic behavior of the summatory functions of λₖ and ...
André Pierro de Camargo
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Möbius-strip-like columnar functional connections are revealed in somato-sensory receptive field centroids [PDF]
Frontiers in Neuroanatomy, 2014 Receptive fields of neurons in the forelimb region of areas 3b and 1 of primary somatosensory cortex, in cats and monkeys, were mapped using extracellular recordings obtained sequentially from nearly radial penetrations. Locations of the field centroids indicated the presence of a functional system in which cortical homotypic representations of the ...
Wright, James Joseph +2 more
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Journal of Physics: Theories and Applications, 2020 The application bispherical coordinates in Schrödinger equation for the Mobius square plus modified Yukawa potential have been obtained. The Schrödinger equation in bispherical coordinates for the separable Mobius square plus modified Yukawa potential ...
Briant Sabathino Harya Wibawa +2 more
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The Möbius function of generalized subword order [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Let $P$ be a poset and let $P^*$ be the set of all finite length words over $P$. Generalized subword order is the partial order on $P^*$ obtained by letting $u≤ w$ if and only if there is a subword $u'$ of $w$ having the same length as $u$ such that ...
Peter R. W. McNamara, Bruce E. Sagan
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Visualization of Mandelbrot and Julia Sets of Möbius Transformations
Fractal and Fractional, 2021 This work reports on a study of the Mandelbrot set and Julia set for a generalization of the well-explored function η(z)=z2+λ. The generalization consists of composing with a fixed Möbius transformation at each iteration step.
Leah K. Mork, Darin J. Ulness
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The Rees product of the cubical lattice with the chain [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We study enumerative and homological properties of the Rees product of the cubical lattice with the chain. We give several explicit formulas for the Möbius function.
Patricia Muldoon, Margaret A. Readdy
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