Results 11 to 20 of about 1,011,636 (279)
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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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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Noncompact harmonic manifolds [PDF]
, 2013 The Lichnerowicz conjecture asserts that all harmonic manifolds are either flat or locally symmetric spaces of rank 1. This conjecture has been proved by Z.I. Szabo for harmonic manifolds with compact universal cover. E. Damek and F.
Knieper, Gerhard, Peyerimhoff, Norbert
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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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Optimal design of single-tuned passive filters using response surface methodology [PDF]
, 2015 This paper presents an approach based on Response Surface Methodology (RSM) to find the optimal parameters of the single-tuned passive filters for harmonic mitigation.
Abdel Aleem, SHE +4 more
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Experimental observation of second-harmonic generation and diffusion inside random media [PDF]
, 2009 We have experimentally measured the distribution of the second-harmonic intensity that is generated inside a highly-scattering slab of porous gallium phosphide. Two complementary techniques for determining the distribution are used.
Ad Lagendijk +25 more
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Bases of exponents with a piecewise linear phase in generalized weighted Lebesgue space
Journal of Inequalities and Applications, 2016 The perturbed system of exponents with a piecewise linear phase, consisting of eigenfunctions of a discontinuous differential operator, is considered in this work.
Tofig Najafov +2 more
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Some Properties of Certain Multivalent Harmonic Functions
Mathematics, 2023 In this paper, various features of a new class of normalized multivalent harmonic functions in the open unit disk are analyzed, including bounds on coefficients, growth estimations, starlikeness and convexity radii.
Georgia Irina Oros +2 more
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Eigenvalues and entropies under the harmonic-Ricci flow [PDF]
, 2013 In this paper, the author discusses the eigenvalues and entropies under the harmonic-Ricci flow, which is the Ricci flow coupled with the harmonic map flow. We give an alternative proof of results for compact steady and expanding harmonic-Ricci breathers.
Li, Yi
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