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), 2024. Published by Science Publishing Group |
Graph Flux Intensity, Electromagnetic Wave, Vicinal Coupling Constant 3JHH [Hz], 3-Sphere, Hopf Fibration, Conic Section, Rectangle, Carnot’s Theorem, Homotopic
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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
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
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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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}
}
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 -
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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