Configurational and conformational analysis with 3-Sphere approach on selective iodination
of α, β-methyl D-ribofuranose (2-α: 2-β) with iodotriphenilphosphonium iodide complex …

Torsional angles calculated with 3-sphere approach from the NMR data (chemical shift δC
[ppm], vicinal coupling constant 3JHH [Hz]) can be used instead of endocyclic torsional …

Dihedral angles are predicted from vicinal coupling constants 3JHH [Hz] with 3-sphere
approach, sphere or torus trigonometric equations of circle 1, 2 and circle inversion 3–5 for …

N-Alkyl-C1-dialkyl chains iminocyclitols with D or L-ribitol stereochemistry are synthesized
with high diastereoselectivity after Grignard reagents addition to N-quaternary pyrrolines …

The shape of the universe, 3-manifold locally reassembles Euclidean 3-dimensional space.
1 A point increasing to a circle is transformed to a torus, 2 able to undergo homotopy, 3 …

The vicinal angle ϕ [deg] is in close relationship with the corresponding dihedral angle
θHnHn+ 1 [deg] under 3-sphere approach, and with tetrahedral angle φ [deg] under …

The wave character of the NMR data (chemical shift ΔδCn [ppm]–vicinal coupling constant
3JHH [Hz]) enable calculation the tandem dihedral-vicinal or tetrahedral-internal angles with …

Tetrahedral angles of five membered ring are disclosed from the polyhedron geometry point
of view, dodecahedron and icosahedron geometry under Fibonacci number. The number of …

The transformation from 4D-3D-2D, from hypersphere-sphere-circle, otherwise from torus to
Dupin cyclide, can be demonstrated with NMR data (carbon chemical shift δCn [ppm], vicinal …

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 …