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On Certain Arithmetic Functions

, 2000
In the recent book there appear certain arithmetic functions which are similar to the Smarandache function. In a recent paper we have considered certain generalization or duals of the Smarandache function. In this note we wish to point out that the arithmetic functions introduced all are particular cases of our function Fj, defined in the following ...
openaire   +2 more sources

Protein Structuromics Reveals a Loop‐Controlled Half‐Open Active Pocket Conformation Throughout Fe(II)/α‐ketoglutarate‐Dependent Dioxygenase Catalytic Cycle

Advanced Science, EarlyView.
This study reveals a conserved half‐open active pocket in Fe(II)/α‐ketoglutarate‐dependent dioxygenases through protein structuromics, distinguished by structural features comprising highly flexible loop elements. Enhanced sampling simulations‐guided mutagenesis experiments elucidated how this flexible loop regulates pocket open/closed conformations ...
Lunjie Wu, Huan Liu, Songyin Zhao, Lei Qin, Jiarui Li, Jun Wang, Zixuan Dai, Jie Gu, Yan Xu, Feiran Li, Yao Nie   +10 more
wiley   +1 more source

Some new arithmetic functions [PDF]

Notes on Number Theory and Discrete Mathematics
We introduce and study some new arithmetic functions, connected with the classical functions φ (Euler's totient), ψ (Dedekind's function) and σ (sum of divisors function).
József Sándor, Krassimir Atanassov
doaj   +1 more source

The Γ-function in the arithmetic of function fields

Duke Mathematical Journal, 1988
Let \({\mathbb{F}}_ q\) denote the finite field of q elements, \(A={\mathbb{F}}_ q[T]\), \(k={\mathbb{F}}_ q(T)\) and denote by \(k_ w\) the completion of k with respect to a valuation w of k. (Thus w is associated with a monic prime of A or, when \(w=\infty\), with 1/T.) The Carlitz zeta function of A is defined by \(\zeta_ A(s)=\sum f^{-s}, \) where ...
openaire   +2 more sources

Automated Extraction of Multicomponent Alloy Data Using Large Language Models for Sustainable Design

Advanced Science, EarlyView.
A large language model (LLM) based pipeline is developed to automatically extract a comprehensive and accurate multicomponent alloy database from literature corpus. The extracted dataset is integrated with sustainability indicators to identify potential alloys that outperform existing industrial benchmark materials in terms of both performance and ...
Aravindan Kamatchi Sundaram, Mohit Chakraborty, Sai Mani Kumar Devathi, B. Pabitramohan Prusty, Rohit Batra   +4 more
wiley   +1 more source

Stem Cell Differentiation Disperses Transcriptional Clusters via a Conserved Surface‐Condensate Trajectory

Advanced Science, EarlyView.
Stem cell differentiation follows a conserved surface condensate trajectory: H3K27ac super enhancers nucleate large RNA polymerase II clusters that grow and unfold before transcriptional activity disperses them. This work reveals how biophysical forces at enhancer surfaces dynamically build and dismantle stem cell transcription hubs, reshaping cell ...
Tim Klingberg, Irina Wachter, Agnieszka Pancholi, Matthias Akyel, Yomna Gohar, Priya Kumar, Ana Miguel Fernandes, Yuzhi Bao, Alica Schmidt‐Heydt, Marcel Piepers, Alicia Günthel, Marcel Sobucki, Elisa Kämmer, Süheyla Eroğlu‐Kayıkçı, Stephan Allgeier, Sylvia Erhardt, Vasily Zaburdaev, Carmelo Ferrai, Lennart Hilbert   +18 more
wiley   +1 more source

Accurately Deciphering Tissue Heterogeneity From Spatial Multi‐Modal and Multi‐Omics With STransformer

Advanced Science, EarlyView.
STransformer is a unified deep learning framework designed to seamlessly accommodate a comprehensive landscape of spatial data. By simultaneously capturing short‐range cellular interactions and tissue‐wide semantic patterns, it extracts robust representations to accurately dissect complex tissue heterogeneity.
Xingyi Li, Jialuo Xu, Gaoyuan Du, Xiangting Jia, Dongmin Zhao, Chunyan Zhou, Kexin Xiao, Jia Gu, Junnan Zhu, Xuequn Shang   +9 more
wiley   +1 more source

Circulating Amino Acid Network Remodeling Reveals Systemic Metabolic Reprogramming Predictive of Colorectal Cancer Recurrence and Metastasis

Advanced Science, EarlyView.
Blood‐based amino acid patterns measured by 19F NMR reveal hidden metabolic changes in colorectal cancer. By analyzing how these amino acids interact as a network, machine learning models identify patients at higher risk of recurrence and metastasis.
Ji‐Yeon Lee, Jumi Kim, Taehan Yoon, So Hyun Kwon, Su Chan Park, Dohyun Chun, Dohyeong Kim, Eun Jung Park, Hyunwoo Kim, Ji Min Lee   +9 more
wiley   +1 more source

Inequalities between some arithmetic functions, II [PDF]

Notes on Number Theory and Discrete Mathematics
As a continuation of Part I (see [1]), we offer new inequalities for classical arithmetic functions such as the Euler's totient function, the Dedekind's psi function, the sum of the positive divisors function, the number of divisors function, extended ...
Krassimir Atanassov, József Sándor, Mladen Vassilev-Missana   +2 more
doaj   +1 more source

Multi‐Targeting Carnosic Acid Kills Drug‐Resistant Helicobacter pylori With Narrow‐Spectrum Activity

Advanced Science, EarlyView.
Carnosic acid selectively eradicates drug‐resistant Helicobacter pylori through a multi‐targeted mechanism involving urease inhibition, membrane disruption, and biofilm eradication. It exhibits no detectable resistance, potent in vivo efficacy, and minimal impact on gut microbiota, positioning it as a promising narrow‐spectrum lead compound against ...
Yuefan Bai, Hongming Huang, Xudong Hang, Shanwei Hu, Qian Tong, Jingchen Xu, Jia Jia, Hongkai Bi   +7 more
wiley   +1 more source