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Symmetry breaking and mismatch in the torsional mechanism of ATP synthesis by F O F 1 -ATP synthase: mathematical number theory proof and its chemical and biological implications.

• Authors : Nath S; Department of Biochemical Engineering and Biotechnology, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India. .

• Source: Theory in biosciences = Theorie in den Biowissenschaften [Theory Biosci] 2024 Dec 22. Date of Electronic Publication: Publisher: Urban & Fischer Country of Publication: Germany NLM ID: 9708216 Publication Model: Print-Electronic Cited Medium: Internet ISSN:

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Number theory, borderline dimension and extensive entropy in distributions of ranked data.

• Authors : Velarde C; Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Mexico City, Mexico.; Robledo A

Subjects: Nonlinear Dynamics* ; Earthquakes*; Entropy

• Source: PloS one [PLoS One] 2022 Dec 27; Vol. 17 (12), pp. e0279448. Date of Electronic Publication: 2022 Dec 27 (Print Publication: 2022).Publisher: Public Library of Science Country of Publication: United States NLM ID: 101285081 Publication Model: eCollection Cited Medium: Internet

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Geometry, number theory, and the butterfly spectrum of two-dimensional Bloch electrons.

• Authors : Satija II; Department of Physics and Astronomy, George Mason University, Fairfax, Virginia 22030, USA.

• Source: Physical review. E [Phys Rev E] 2021 Oct; Vol. 104 (4-1), pp. 044205.Publisher: American Physical Society Country of Publication: United States NLM ID: 101676019 Publication Model: Print Cited Medium: Internet ISSN:

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p-Adic morphology, biomorphic structures and number theory.

• Authors : Ignatov VV; Independent Scholar, 125222, Moscow, Box#57, Russia. Electronic address: .

Subjects: Mathematics* ; Models, Biological* ; Morphogenesis*

• Source: Bio Systems [Biosystems] 2021 Jul; Vol. 205, pp. 104404. Date of Electronic Publication: 2021 Mar 27.Publisher: Elsevier Science Ireland Country of Publication: Ireland NLM ID: 0430773 Publication Model: Print-Electronic Cited Medium: Internet ISSN:

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On generating functions in additive number theory, II: lower-order terms and applications to PDEs.

• Authors : Brandes J; Mathematical Sciences, University of Gothenburg and Chalmers Institute of Technology, 412 96 Göteborg, Sweden.; Parsell ST

• Source: Mathematische annalen [Math Ann] 2021; Vol. 379 (1), pp. 347-376. Date of Electronic Publication: 2020 Dec 23.Publisher: J. Springer [etc.] Country of Publication: Germany NLM ID: 9876285 Publication Model: Print-Electronic Cited Medium: Print ISSN:

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Effective Number Theory: Counting the Identities of a Quantum State.

• Authors : Horváth I; Department of Anesthesiology and Department of Physics, University of Kentucky, Lexington, KY 40536, USA.; Mendris R

• Source: Entropy (Basel, Switzerland) [Entropy (Basel)] 2020 Nov 10; Vol. 22 (11). Date of Electronic Publication: 2020 Nov 10.Publisher: MDPI Country of Publication: Switzerland NLM ID: 101243874 Publication Model: Electronic Cited Medium: Internet ISSN: 1099-4300

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Using Figurate Numbers in Elementary Number Theory - Discussing a 'Useful' Heuristic From the Perspectives of Semiotics and Cognitive Psychology.

• Authors : Kempen L; Department of Mathematics, University of Rostock, Rostock, Germany.; Biehler R

• Source: Frontiers in psychology [Front Psychol] 2020 Jun 17; Vol. 11, pp. 1180. Date of Electronic Publication: 2020 Jun 17 (Print Publication: 2020).Publisher: Frontiers Research Foundation Country of Publication: Switzerland NLM ID: 101550902 Publication Model: eCollection Cited Medium: Print

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Mathematical proof that rocked number theory will be published.

• Authors : Castelvecchi D

• Source: Nature [Nature] 2020 Apr; Vol. 580 (7802), pp. 177.Publisher: Nature Publishing Group Country of Publication: England NLM ID: 0410462 Publication Model: Print Cited Medium: Internet ISSN:

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On the resilience of magic number theory for conductance ratios of aromatic molecules.

• Authors : Ulčakar L; Jožef Stefan Institute, Ljubljana, Slovenia.; Rejec T

• Source: Scientific reports [Sci Rep] 2019 Mar 05; Vol. 9 (1), pp. 3478. Date of Electronic Publication: 2019 Mar 05.Publisher: Nature Publishing Group Country of Publication: England NLM ID: 101563288 Publication Model: Electronic Cited Medium: Internet ISSN:

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Number-theory prodigy among winners of most coveted prize in mathematics.

• Authors : Castelvecchi D

• Source: Nature [Nature] 2018 Aug; Vol. 560 (7717), pp. 152-153.Publisher: Nature Publishing Group Country of Publication: England NLM ID: 0410462 Publication Model: Print Cited Medium: Internet ISSN:

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