Results 51 to 60 of about 39,406 (264)
On the number of harmonic frames
Applied and Computational Harmonic Analysis, 2020 There is a finite number $h_{n,d}$ of tight frames of $n$ distinct vectors for $\mathbb{C}^d$ which are the orbit of a vector under a unitary action of the cyclic group $\mathbb{Z}_n$. These cyclic harmonic frames (or geometrically uniform tight frames) are used in signal analysis and quantum information theory, and provide many tight frames of ...
Simon Marshall, Shayne Waldron
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Loss of IGF‐1R impairs DNA‐PKcs recruitment to chromatin leading to defective end‐joining
Molecular Oncology, EarlyView.IGF‐1R promotes radioresistance by facilitating DNA‐PKcs recruitment to chromatin, enabling non‐homologous end‐joining (NHEJ) repair of double‐strand breaks. Inhibition or loss of IGF‐1R disrupts this recruitment to damage sites, driving compensatory reliance on microhomology‐mediated end‐joining (MMEJ) repair.
Matthew O. Ellis +3 more
wiley +1 more source
Molecular Oncology, EarlyView.Single‐cell multi‐omics reveals epigenetic heterogeneity across therapy‐adaptive tumor states, including quiescent/dormant, drug‐tolerant persister, and EMT‐like phenotypes. By linking regulatory features with state‐associated biomarkers, these approaches inform biomarker‐guided therapeutic strategies for evolving tumors.
Hee Jung Kim +3 more
wiley +1 more source
Hypergeometric series and harmonic number identities
Advances in Applied Mathematics, 2005 10 ...
CHU, Wenchang, DEDONNO L.
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Odd harmonic numbers exceed 10²⁴ [PDF]
Mathematics of Computation, 2010 A number n > 1 n>1
Graeme L. Cohen, Ronald M. Sorli
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Molecular Oncology, EarlyView.Matched spatial transcriptomics and single‐nuclei RNA‐seq were generated for anaplastic and BRAFV600E papillary thyroid cancers revealing generic and tumor‐specific states occurring in cancer cells and in the tumor microenvironment. In this context, cancer dedifferentiation mirrored organoid maturation through ordered thyroid marker gain/loss ...
Adrien Tourneur +11 more
wiley +1 more source
Binomial Series Involving Harmonic-like Numbers
AxiomsBy 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
Abel's Lemma and Identities on Harmonic Numbers
Integers, 2014 Recently, Chen, Hou and Jin used both Abel's lemma on summation by parts and Zeilberger's algorithm to generate recurrence relations for definite summations. Meanwhile, they proposed the Abel-Gosper method to evaluate some indefinite sums involving harmonic numbers.
Hai-Tao Jin, Daniel K. Du
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Gut microbiota alterations in patients with non‐small‐cell lung cancer undergoing chemoradiotherapy
Molecular Oncology, EarlyView.We investigated the impact of concurrent chemoradiotherapy (CRT) on the gut microbiota in patients with locally advanced non‐small‐cell lung cancer. Overall gut microbiota composition remained largely stable throughout CRT while antibiotic exposure may influence microbial diversity.
Hanne Marte Nymoen +19 more
wiley +1 more source
Differences of Harmonic Numbers and the abc-Conjecture
The PUMP Journal of Undergraduate Research, 2018 Our main source of inspiration was a talk by Hendrik Lenstra on harmonic numbers, which are numbers whose only prime factors are two or three. Gersonides proved 675 years ago that one can be written as a difference of harmonic numbers in only four ways: 2-1, 3-2, 4-3, and 9-8.
da Silva, Natalia +2 more
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