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Graph Flux Intensity and Electromagnetic Wave on 3-sphere Approach

Received: 26 October 2023     Accepted: 10 November 2023     Published: 21 November 2023
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Abstract

3-Sphere characteristic angles (θnN with n = 1-6, and ϕnN with n = 1, 2, N = A, B, C, CA, CB) are calculated from NMR data, the differences in chemical shifts between two atoms of carbon ΔδCnCn+1 [ppm] and vicinal coupling constant 3JHnHn+1 [Hz], using I. Graph-flux intensity, Golden ratio of pentagon, II. radio wave, III. Homotopic approach, exploring electromagnetic field of five membered iminocyclitols 1-3. Fibonacci’s numbers calculated with Plank constant h and h-bar are compared and used for determination of the tetrahedral angles. Attempts to obtain the best equation for calculation the energy from carbon chemical shift: the square EP2 = (Δδxω)2xhxNA[Jx10-3xrad/sxmoli] and the cube of frequency EP3 = (Δδxω)3xhxNA[Jxrad/s2xmoli = WattxHzxrad/moli] are compared with Plank-Einstain equation EP1 = ΔδxωxhxNA[Jx10-6xrad/moli]. Continues transformation from torus to rectangle (f), and from rectangle to torus (f-1), is a homotopic process, able to used polyhedron number in rad or radieni (π). The wave character of NMR data shown interesting relationship between angles on 3-Sphere units approach. Bond distances lCnCn+1[A0] of five membered ring iminocyclitols 1, 2 are calculated from dihedral angles θHnHn+1[deg]. Methods for calculation of the vicinal coupling constant 3JHH [Hz] with 3-Sphere – Polar equation – Conic section - Lie algebra - Hopf fibration, are disclosed from the mathematic point of view and in far field from physics electromagnetic radiation point of view.

Published in Science Journal of Chemistry (Volume 11, Issue 6)
DOI 10.11648/j.sjc.20231106.12
Page(s) 212-225
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2023. Published by Science Publishing Group

Keywords

Graph Flux Intensity, Electromagnetic Wave, Vicinal Coupling Constant 3JHH [Hz], 3-Sphere, Hopf Fibration, Conic Section, Rectangle, Carnot’s Theorem, Homotopic

References
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Cite This Article
  • APA Style

    Mitan, C., Bartha, E., Filip, P., Caproiu, M., Draghici, C., et al. (2023). Graph Flux Intensity and Electromagnetic Wave on 3-sphere Approach. Science Journal of Chemistry, 11(6), 212-225. https://doi.org/10.11648/j.sjc.20231106.12

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    ACS Style

    Mitan, C.; Bartha, E.; Filip, P.; Caproiu, M.; Draghici, C., et al. Graph Flux Intensity and Electromagnetic Wave on 3-sphere Approach. Sci. J. Chem. 2023, 11(6), 212-225. doi: 10.11648/j.sjc.20231106.12

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    AMA Style

    Mitan C, Bartha E, Filip P, Caproiu M, Draghici C, et al. Graph Flux Intensity and Electromagnetic Wave on 3-sphere Approach. Sci J Chem. 2023;11(6):212-225. doi: 10.11648/j.sjc.20231106.12

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  • @article{10.11648/j.sjc.20231106.12,
      author = {Carmen-Irena Mitan and Emerich Bartha and Petru Filip and Miron-Teodor Caproiu and Constantin Draghici and Robert Michael Moriarty},
      title = {Graph Flux Intensity and Electromagnetic Wave on 3-sphere Approach},
      journal = {Science Journal of Chemistry},
      volume = {11},
      number = {6},
      pages = {212-225},
      doi = {10.11648/j.sjc.20231106.12},
      url = {https://doi.org/10.11648/j.sjc.20231106.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjc.20231106.12},
      abstract = {3-Sphere characteristic angles (θnN with n = 1-6, and ϕnN with n = 1, 2, N = A, B, C, CA, CB) are calculated from NMR data, the differences in chemical shifts between two atoms of carbon ΔδCnCn+1 [ppm] and vicinal coupling constant 3JHnHn+1 [Hz], using I. Graph-flux intensity, Golden ratio of pentagon, II. radio wave, III. Homotopic approach, exploring electromagnetic field of five membered iminocyclitols 1-3. Fibonacci’s numbers calculated with Plank constant h and h-bar are compared and used for determination of the tetrahedral angles. Attempts to obtain the best equation for calculation the energy from carbon chemical shift: the square EP2 = (Δδxω)2xhxNA[Jx10-3xrad/sxmoli] and the cube of frequency EP3 = (Δδxω)3xhxNA[Jxrad/s2xmoli = WattxHzxrad/moli] are compared with Plank-Einstain equation EP1 = ΔδxωxhxNA[Jx10-6xrad/moli]. Continues transformation from torus to rectangle (f), and from rectangle to torus (f-1), is a homotopic process, able to used polyhedron number in rad or radieni (π). The wave character of NMR data shown interesting relationship between angles on 3-Sphere units approach. Bond distances lCnCn+1[A0] of five membered ring iminocyclitols 1, 2 are calculated from dihedral angles θHnHn+1[deg]. Methods for calculation of the vicinal coupling constant 3JHH [Hz] with 3-Sphere – Polar equation – Conic section - Lie algebra - Hopf fibration, are disclosed from the mathematic point of view and in far field from physics electromagnetic radiation point of view.
    },
     year = {2023}
    }
    

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  • TY  - JOUR
    T1  - Graph Flux Intensity and Electromagnetic Wave on 3-sphere Approach
    AU  - Carmen-Irena Mitan
    AU  - Emerich Bartha
    AU  - Petru Filip
    AU  - Miron-Teodor Caproiu
    AU  - Constantin Draghici
    AU  - Robert Michael Moriarty
    Y1  - 2023/11/21
    PY  - 2023
    N1  - https://doi.org/10.11648/j.sjc.20231106.12
    DO  - 10.11648/j.sjc.20231106.12
    T2  - Science Journal of Chemistry
    JF  - Science Journal of Chemistry
    JO  - Science Journal of Chemistry
    SP  - 212
    EP  - 225
    PB  - Science Publishing Group
    SN  - 2330-099X
    UR  - https://doi.org/10.11648/j.sjc.20231106.12
    AB  - 3-Sphere characteristic angles (θnN with n = 1-6, and ϕnN with n = 1, 2, N = A, B, C, CA, CB) are calculated from NMR data, the differences in chemical shifts between two atoms of carbon ΔδCnCn+1 [ppm] and vicinal coupling constant 3JHnHn+1 [Hz], using I. Graph-flux intensity, Golden ratio of pentagon, II. radio wave, III. Homotopic approach, exploring electromagnetic field of five membered iminocyclitols 1-3. Fibonacci’s numbers calculated with Plank constant h and h-bar are compared and used for determination of the tetrahedral angles. Attempts to obtain the best equation for calculation the energy from carbon chemical shift: the square EP2 = (Δδxω)2xhxNA[Jx10-3xrad/sxmoli] and the cube of frequency EP3 = (Δδxω)3xhxNA[Jxrad/s2xmoli = WattxHzxrad/moli] are compared with Plank-Einstain equation EP1 = ΔδxωxhxNA[Jx10-6xrad/moli]. Continues transformation from torus to rectangle (f), and from rectangle to torus (f-1), is a homotopic process, able to used polyhedron number in rad or radieni (π). The wave character of NMR data shown interesting relationship between angles on 3-Sphere units approach. Bond distances lCnCn+1[A0] of five membered ring iminocyclitols 1, 2 are calculated from dihedral angles θHnHn+1[deg]. Methods for calculation of the vicinal coupling constant 3JHH [Hz] with 3-Sphere – Polar equation – Conic section - Lie algebra - Hopf fibration, are disclosed from the mathematic point of view and in far field from physics electromagnetic radiation point of view.
    
    VL  - 11
    IS  - 6
    ER  - 

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Author Information
  • Organic Chemistry, Institute of Organic and Supramolecular Chemistry, Bucharest, Romania

  • Organic Chemistry, Institute of Organic and Supramolecular Chemistry, Bucharest, Romania

  • Organic Chemistry, Institute of Organic and Supramolecular Chemistry, Bucharest, Romania

  • Organic Chemistry, Institute of Organic and Supramolecular Chemistry, Bucharest, Romania

  • Organic Chemistry, Institute of Organic and Supramolecular Chemistry, Bucharest, Romania

  • Organic Chemistry, University of Illinois at Chicago, Chicago, USA

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