Results 61 to 70 of about 37,250 (282)

Series associated with harmonic numbers, Fibonacci numbers and central binomial coefficients $binom{2n}{n}$ [PDF]

Notes on Number Theory and Discrete Mathematics
We find various series that involve the central binomial coefficients $binom{2n}{n}$, harmonic numbers and Fibonacci numbers. Contrary to the traditional hypergeometric function _pF_q approach, our method utilizes a straightforward transformation to ...
Segun Olofin Akerele, Olamide Esther Salami   +1 more
doaj   +1 more source

Perspectives in educating molecular pathologists on liquid biopsy: Toward integrative, equitable, and decentralized precision oncology

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, Umberto Malapelle, Catherine Alix‐Panabières, Claus Lindbjerg Andersen, Sandra Chlebowski, Vivien Lake, Caroline Lacoux, Virginie Lespinet‐Fabre, Olivier Bordone, Simon Heeke, Christophe Bontoux, Ellen Heitzer, Klaus Pantel, Paul Hofman   +13 more
wiley   +1 more source

LINC01116, a hypoxia‐lncRNA marker of pathological lymphangiogenesis and poor prognosis in lung adenocarcinoma

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, Rafael Lopes Goncalves, Marin Truchi, Caroline Lacoux, Célia Scribe, Hugo Cadis, Laetitia Guardini, Sophie Bekisz, Marius Ilié, Paul Hofman, Georges Vassaux, Bernard Mari, Roger Rezzonico   +12 more
wiley   +1 more source

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
openaire   +2 more sources

Infrared laser sampling of low volumes combined with shotgun lipidomics reveals lipid markers in palatine tonsil carcinoma

Molecular Oncology, EarlyView.
Nanosecond infrared laser (NIRL) low‐volume sampling combined with shotgun lipidomics uncovers distinct lipidome alterations in oropharyngeal squamous cell carcinoma (OPSCC) of the palatine tonsil. Several lipid species consistently differentiate tumor from healthy tissue, highlighting their potential as diagnostic markers.
Leonard Kerkhoff, Manuela Moritz, Dennis Eggert, Anna Worthmann, Joerg Heeren, Henrike Zech, Till S. Clauditz, Waldemar Wilczak, Hartmut Schlüter, Christian S. Betz, Arne Böttcher, Jan Hahn   +11 more
wiley   +1 more source

Network divergence analysis identifies adaptive gene modules and two orthogonal vulnerability axes in pancreatic cancer

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, Lyanne Delgado‐Coka, Natalia Marchenko, Luisa F. Escobar‐Hoyos, Kenneth R. Shroyer, Alisa Yurovsky, Trey Ideker, Gabor Balázsi, Thomas MacCarthy, Scott Powers   +9 more
wiley   +1 more source

Binomial Series Involving Harmonic-like Numbers

Axioms
By computing definite integrals, we shall examine binomial series of convergence rate ±1/2 and weighted by harmonic-like numbers. Several closed formulae in terms of the Riemann and Hurwitz zeta functions as well as logarithm and polylogarithm functions ...
Chunli Li, Wenchang Chu
doaj   +1 more source

Approximations of the Harmonic Numbers

Results in Mathematics
Abstract 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
openaire   +1 more source

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.
openaire   +1 more source

Pre‐analytical optimization of cell‐free DNA and extracellular vesicle‐derived DNA for mutation detection in liquid biopsies

Molecular Oncology, EarlyView.
Pre‐analytical handling critically determines liquid biopsy performance. This study defines practical best‐practice conditions for cell‐free DNA (cfDNA) and extracellular vesicle–derived DNA (evDNA), showing how processing time, storage conditions, tube type, and plasma input volume affect DNA integrity and mutation detection.
Jonas Dohmen, Lucrezia De Santis, Bret M. Stephens, Vincent Bernard, Jörg C. Kalff, Lara Braun, Phillipp Leyendecker, Johannes Röttgen, Daniel Weissinger, Anirban Maitra, Paola A. Guerrero, Alexander Semaan   +11 more
wiley   +1 more source