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Journal of Knot Theory and Its Ramifications, 2016 The harmonic knot [Formula: see text] is parametrized as [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are pairwise coprime integers and [Formula: see text] is the degree [Formula: see text] Chebyshev polynomial of the first kind. We classify the harmonic knots [Formula: see text] for [Formula: see text] We
Koseleff, Pierre-Vincent, Pecker, Daniel
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International Journal of Modern Physics A, 2000 The harmonic polylogarithms (hpl's) are introduced. They are a generalization of Nielsen's polylogarithms, satisfying a product algebra (the product of two hpl's is in turn a combination of hpl's) and forming a set closed under the transformation of the arguments x=1/z and x=(1-t)/(1+t). The coefficients of their expansions and their Mellin transforms
Remiddi, Ettore +1 more
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Harmonicity of the inverse of a harmonic diffeomorphism
Journal of Mathematical Analysis and Applications, 2012 AbstractIn this paper we obtain a necessary and sufficient condition for the harmonicity of the inverse of a harmonic diffeomorphism. As an application, we give explicit representations of reversible logharmonic diffeomorphisms. As another application, we connect the harmonicity of the inverse of a hyperbolic harmonic quasiconformal diffeomorphism with
Xingdi Chen, Ainong Fang
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Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions [PDF]
Abstract and Applied Analysis, 2012 For Riemannian manifolds M and N, admitting a submersion ϕ with compact fibres, we introduce the projection of a function via its decomposition into horizontal and vertical components. By comparing the Laplacians on M and N, we determine conditions under which a harmonic function on U = ϕ−1(V) ⊂ M projects down, via its horizontal component, to a ...
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Harmonic Causation and Harmonic Echoes [PDF]
Nature, 1873 IN reference to the question of “Harmonic Echoes,” allow me to suggest to those who may have the opportunity of observation, how desirable it is that these echo-tones should be investigated in a manner to determine whether they are truly harmonic or not. There would be no difficulty in testing the sounds given in response to the notes of a closed organ-
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Harmonic conjugation in harmonic matroids
Discrete Mathematics, 2009 This paper was finished in 2008.
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The Approximation of Harmonic Functions by Harmonic Polynomials and by Harmonic Rational Functions [PDF]
Bulletin of the American Mathematical Society, 1929 which converges uniformly f or all values of 6. This is of course a general fact, tha t if a given function can be uniformly approximated as closely as desired by a linear combination of other functions, then that function can be expanded in a uniformly convergent series of which each term is a linear combination of those other functions, and ...
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Harmonic analysis of harmonic functions in the plane [PDF]
Proceedings of the American Mathematical Society, 1976 A continuous function on the complex plane is harmonic if and only if the span of its compositions with entire functions is not dense in the space of continuous functions in the topology of uniform convergence on compact sets.
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Weighted Tutte-Grothendieck polynomials of graphs [PDF]
arXiv, 2022 In this paper, we introduce the concept of the weighted (harmonic) chromatic polynomials of graphs and discuss some of its properties. We also present the notion of the weighted (harmonic) Tutte--Grothendieck polynomials of graphs and give a generalization of the recipe theorem between the harmonic Tutte--Grothendieck polynomials graphs and the ...
arxiv