Graph Flux Intensity and Electromagnetic Wave on 3-sphere Approach

Carmen-Irena Mitan; Emerich Bartha; Petru Filip; Miron-Teodor Caproiu; Constantin Draghici; Robert Michael Moriarty

doi:doi:10.11648/j.sjc.20231106.12

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Graph Flux Intensity and Electromagnetic Wave on 3-sphere Approach

Carmen-Irena Mitan^*, Emerich Bartha, Petru Filip, Miron-Teodor Caproiu, Constantin Draghici, Robert Michael Moriarty

Published in Science Journal of Chemistry (Volume 11, Issue 6)

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

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Abstract

3-Sphere characteristic angles (θ^nN with n = 1-6, and ϕ_nN 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 Δδ_CnCn+1 [ppm] and vicinal coupling constant ³J_HnHn+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 E^P2 = (Δδxω)²xhxN_A[Jx10^-3xrad/sxmoli] and the cube of frequency E^P3 = (Δδxω)³xhxN_A[Jxrad/s²xmoli = WattxHzxrad/moli] are compared with Plank-Einstain equation E^P1 = ΔδxωxhxN_A[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 l_CnCn+1[A⁰] of five membered ring iminocyclitols 1, 2 are calculated from dihedral angles θ_HnHn+1[deg]. Methods for calculation of the vicinal coupling constant ³J_HH [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 ³J_HH [Hz], 3-Sphere, Hopf Fibration, Conic Section, Rectangle, Carnot’s Theorem, Homotopic

References

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[26]	C.-I. Mitan, E. Bartha, C. Draghici, M. T. Caproiu, P. Filip, R. M. Moriarty, Hopf fibration and Huchel theories on torsional angles, 257^th ACS National Meeting in Orlando, Florida, March 31- April 4, 2019, CARB 39. Publisher: American Chemical Society, Washington, D. C.
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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

Carmen-Irena Mitan

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

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Emerich Bartha

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

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Petru Filip

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

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Miron-Teodor Caproiu

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

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Constantin Draghici

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

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Robert Michael Moriarty

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

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Plain Text BibTeX RIS

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

Copy | Download

@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}
}

Copy | Download

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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