Results 21 to 30 of about 11,829,477 (307)

Harmonic Forms and Spinors on the Taub-bolt Space [PDF]

, 2019
This paper studies the space of $L ^2 $ harmonic forms and $L ^2 $ harmonic spinors on Taub-bolt, a Ricci-flat Riemannian 4-manifold of ALF type. We prove that the space of harmonic square-integrable 2-forms on Taub-bolt is 2-dimensional and construct a ...
Franchetti, Guido
core   +2 more sources

Median Bernoulli Numbers and Ramanujan’s Harmonic Number Expansion

Mathematics, 2022
Ramanujan-type harmonic number expansion was given by many authors. Some of the most well-known are: Hn∼γ+logn−∑k=1∞Bkk·nk, where Bk is the Bernoulli numbers.
Kwang-Wu Chen
doaj   +1 more source

Algebraic Relations Between Harmonic Sums and Associated Quantities [PDF]

, 2003
We derive the algebraic relations of alternating and non-alternating finite harmonic sums up to the sums of depth~6. All relations for the sums up to weight~6 are given in explicit form.
Anastasiou, Anastasiou, Anastasiou, Anastasiou, Anastasiou, Anastasiou, Anastasiou, Anastasiou, Anastasiou, Arbuzov, Baikov, Baikov, Berends, Berends, Bern, Bern, Bern, Bern, Bern, Bern, Berndt, Berstel, Bigotte, Binoth, Blümlein, Blümlein, Blümlein, Blümlein, Blümlein, Blümlein, Bonciani, Borwein, Borwein, Borwein, Bowman, Broadhurst, Broadhurst, Catani, Catani, Clebsch, Davydychev, Davydychev, Davydychev, Devoto, Eilenburg, Euler, Euler, Field, Fleischer, Fleischer, Fleischer, Fleischer, Fleischer, Furmanski, Fàa di Bruno, Garland, Garland, Gastmans, Gauss, Gehrmann, Glover, Glover, Glover, Goncharov, Gonzalez-Arroyo, Gonzalez-Arroyo, Gordan, Hamberg, Hamberg, Hardy, Harlander, Harlander, Harlander, Hoang Ngoc Minh, Hoang Ngoc Minh, Hoffman, Hopf, Jegerlehner, Jegerlehner, Johannes Blümlein, Kalmykov, Kassel, Kazakov, Kazakov, Kölbig, Kölbig, Lang, Larin, Larin, Larin, Lewin, Lewin, Lidl, Lothaire, Lothaire, Lugowski, Lyndon, Lyndon, Macdonald, MacLane, Matsuura, Matsuura, Matsuura, Matsuura, Milner, Moch, Moch, Moch, Moch, Müller, Nielsen, Radford, Ravindran, Ravindran, Remiddi, Retey, Reutenauer, Rijken, Rijken, Rijken, Rijken, Rijken, Rijken, Sanchez Guillen, Schwartz, Sita Ramachandra Rao, Sloane, Sloane, Smirnov, Smirnov, Smirnov, Smirnov, Sweedler, Tarasov, Tausk, van Neerven, van Neerven, van Neerven, van Neerven, van Neerven, van Neerven, Vermaseren, Vermaseren, Vladimirov, Waldschmidt, Weinzierl, Weinzierl, Witt, Witt, Yoshida, Zagier, Zijlstra, Zijlstra, Zijlstra, Zijlstra, Zijlstra, Zudilin   +156 more
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On the denominators of harmonic numbers, III [PDF]

Periodica Mathematica Hungarica, 2022
Let ℒ be the set of all positive integers n such that the denominator of 1+1/2+⋯+1/n is less than the least common multiple of 1,2,⋯,n. In this paper, under a certain assumption on linear independence, we prove that the set ℒ has the upper asymptotic density 1. The assumption follows from Schanuel’s conjecture.
Wu, Bing-Ling, Yan, Xiao-Hui
openaire   +3 more sources

rf acceleration with harmonic number jump

Physical Review Special Topics. Accelerators and Beams, 2006
We have recently considered acceleration of protons and heavy ions in a fixed-field alternating-gradient accelerator with nonscaling lattice and linear field profile.
Alessandro G. Ruggiero
doaj   +1 more source

Harmonic numbers, harmonic series and zeta function [PDF]

Moroccan Journal of Pure and Applied Analysis, 2018
AbstractThis paper reviews, from different points of view, results on Bernoulli numbers and polynomials, the distribution of prime numbers in connexion with the Riemann hypothesis. We give an account on the theorem of G. Robin, as formulated by J. Lagarias. The other parts are devoted to the series𝒨is(z)=∑n=1∞μ(n)nszn$\mathcal{M}{i_s}(z) = \sum\limits_{
openaire   +2 more sources

Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications

Mathematics, 2019
In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermite⁻Hadamard inequality for functions whose absolute values of the second (resp. first) derivatives to positive real powers are log-convex.
Shilpi Jain, Khaled Mehrez, Dumitru Baleanu, Praveen Agarwal   +3 more
doaj   +1 more source

Analysis and application of real-time compensation of positioning precision of the turntable with a harmonic function [PDF]

Metrology and Measurement Systems, 2022
In order to guarantee the accuracy of turntable angle measurement, a real-time compensation method for turntable positioning precision based on harmonic analysis is proposed in this paper.
Yi Zhou, Weibin Zhu, Yi Shu, Yao Huang, Wei Zou, Zi Xue   +5 more
doaj   +1 more source

Some identities involving harmonic numbers [PDF]

Mathematics of Computation, 1990
Let H n {H_n} denote the nth harmonic number. Explicit formulas for sums of the form ∑ a k H k \sum {a_k}{H_k} or ∑ a
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On some series involving harmonic and skew-harmonic numbers

Journal of Classical Analysis, 2023
In this paper, we evaluate in closed form several different series involving the harmonic numbers and skew-harmonic numbers. We consider two classes of series involving these sequences. One class of series involves the product of the $n$th harmonic or skew-harmonic number and a tail.
openaire   +2 more sources