Results 51 to 60 of about 106,566 (267)

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
openaire   +3 more sources

Combinatorial Identities with Multiple Harmonic-like Numbers

AppliedMath
Multiple 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
doaj   +1 more source

Epigenetic heterogeneity and plasticity in therapy‐induced tumor states through single‐cell multi‐omics

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, Hwiyeong Lee, Jin Hong, Daechan Park   +3 more
wiley   +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

Spatial and single‐nuclei transcriptomics reveals idiosyncratic and generic patterns in papillary and anaplastic thyroid cancers

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, Joel Rodrigues Vitória, Manuel Saiselet, Ligia Craciun, Denis Larsimont, Anne Lefort, Frédérick Libert, Carine Maenhaut, Sabine Costagliola, Maxime Tarabichi, Mirian Romitti, Vincent Detours   +11 more
wiley   +1 more source

Hypergeometric series and harmonic number identities

Advances in Applied Mathematics, 2005
10 ...
CHU, Wenchang, DEDONNO L.
openaire   +4 more sources

Odd harmonic numbers exceed 10²⁴ [PDF]

Mathematics of Computation, 2010
A number n > 1 n>1
Graeme L. Cohen, Ronald M. Sorli
openaire   +3 more sources

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, Zhi Zhao, Henrik Horndalsveen, Maria Moksnes Bjaanæs, Bjørn Henning Grønberg, Tarje Halvorsen, Tesfaye Madebo, Marianne Aanerud, Jussi Koivunen, Kersti Oselin, Saulius Cicenas, Nina Helbekkmo, Jarkko Ahvonen, Maria Silvoniemi, Tine Norman Alver, Tonje Dalen, Åsa Kristina Öjlert, Saima Jamil Farooqi, Åslaug Helland, Vilde Drageset Haakensen   +19 more
wiley   +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
openaire   +5 more sources

Evaluating Infinite Series Involving Harmonic Numbers by Integration

Mathematics
Eight 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
doaj   +1 more source