Science Journal of Chemistry

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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.

DOI 10.11648/j.sjc.20231106.12
Published in Science Journal of Chemistry (Volume 11, Issue 6, December 2023)
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), 2024. 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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