Results 51 to 60 of about 98,048 (175)
Molecular Oncology, EarlyView.Tumors contain diverse cellular states whose behavior is shaped by context‐dependent gene coordination. By comparing gene–gene relationships across biological contexts, we identify adaptive transcriptional modules that reorganize into distinct vulnerability axes.
Brian Nelson +9 more
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All harmonic numbers less than 1014 [PDF]
Japan Journal of Industrial and Applied Mathematics, 2007 ``A positive integer \(n\) is said to be \textit{harmonic} if the harmonic mean of its positive divisors \[ H(n)=\frac{n\tau(n)}{\sigma(n)} \] is an integer, where \(\tau(n)\) denotes the number of the positive divisors of \(n\).'' Properties of harmonic numbers, including their relationship to perfect numbers, have been studied by \textit{Ø. Ore} [Am.
Goto, Takeshi, Okeya, Katsuyuki
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Evaluating Infinite Series Involving Harmonic Numbers by Integration
MathematicsEight infinite series involving harmonic-like numbers are coherently and systematically reviewed. They are evaluated in closed form exclusively by integration together with calculus and complex analysis. In particular, a mysterious series W is introduced
Chunli Li, Wenchang Chu
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Approximations of the Harmonic Numbers
Results in MathematicsAbstract The aim of this paper is to present some approximations on the harmonic numbers. Some associated asymptotic series are constructed.
Chao-Ping Chen, Cristinel Mortici
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On Spieß’s conjecture on harmonic numbers
Discrete Applied Mathematics, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jin, Hai-Tao, Sun, Lisa H.
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Optimal Harmonic Period Assignment With Constrained Number of Distinct Period Values
IEEE Access, 2020 Harmonic periods have been of great importance in the design of real-time applications due to their high schedulability, predictability, and ease of analysis.
Ivan Pavic, Hrvoje Dzapo
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IEEE Access, 2020 As effective measures of energy savings and emission reduction, non-linear loads, such as variable-frequency drives, are widely used. However, the problem of harmonic pollution in power systems is becoming increasingly severe.
Zhihua Zhang, Zeqi Qu, Jie Yang
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Asymptotic inequalities for alternating harmonics [PDF]
Bulletin of Mathematical Sciences, 2019 For n ∈ ℕ the nth alternating harmonic number Hn∗ :=∑ k=1n(−1)k−1 1 k is given in the form Hn∗ =ln 2 + (−1)n+1 4⌊n+1 2 ⌋ +∑i=1q−1 (4i − 1)B 2i (2i)(2⌊n+1 2 ⌋)2i + rq(n), where q ∈ ℕ is a parameter controlling the magnitude of the error term rq ...
Vito Lampret
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Cubic harmonics and Bernoulli numbers
Journal of Combinatorial Theory, Series A, 2012 18 pages, 3 ...
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