Results 71 to 80 of about 10,640,447 (355)
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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Molecular Oncology, EarlyView.Development of therapies targeting cancer‐associated fibroblasts (CAFs) necessitates preclinical model systems that faithfully represent CAF–tumor biology. We established an in vitro coculture system of patient‐derived pancreatic CAFs and tumor cell lines and demonstrated its recapitulation of primary CAF–tumor biology with single‐cell transcriptomics ...
Elysia Saputra +10 more
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Odd Euler Sums and Harmonic Series with Cubic Central Binomial Coefficients in Denominators
AxiomsBy means of the coefficient extraction method, we examine a transformation of a classical hypergeometric series. Three classes of infinite series (of convergence rate “1/4”) with harmonic numbers in numerators and cubic central binomial coefficients in ...
Chunli Li, Wenchang Chu
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Molecular Oncology, EarlyView.Liquid biopsy enables minimally invasive, real‐time molecular profiling through analysis of circulating biomarkers in biological fluids. This Perspective highlights the importance of training pathologists through integrative educational programs, such as the European Masters in Molecular Pathology, to ensure effective and equitable implementation of ...
Marius Ilié +13 more
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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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Molecular Oncology, EarlyView.The LINC01116 long noncoding RNA is induced by hypoxia and associated with poor prognosis and high recurrence rates in two cohorts of lung adenocarcinoma patients. Here, we demonstrate that besides its expression in cancer cells, LINC01116 is markedly expressed in lymphatic endothelial cells of the tumor stroma in which it participates in hypoxia ...
Marine Gautier‐Isola +12 more
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Molecular Oncology, EarlyView.The cancer problem is increasing globally with projections up to the year 2050 showing unfavourable outcomes in terms of incidence and cancer‐related deaths. The main challenges are prevention, improved therapeutics resulting in increased cure rates and enhanced health‐related quality of life.
Ulrik Ringborg +43 more
wiley +1 more source
Combinatorial Identities with Multiple Harmonic-like Numbers
AppliedMathMultiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters.
Kunle Adegoke, Robert Frontczak
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