In the imidazo[2,1-b][1,3]thia-zole group of the title compound, C(21)H(17)ClN(4)O(2)S, the dihedral angle between the thia-zole and imidazole rings is 1.9 (2)°. The mean plane of this group makes dihedral angles of 5.5 (2) and 39.9 (2)° with the benzene rings of the chloro-phenyl and meth-oxy-phenyl groups, respectively. The dihedral angle between these two benzene rings is 34.4 (2)°. In the c...

Focusing on scattering from natural media, dihedral (double bounce) scattering is often characterized as a soil-trunk double Fresnel reflection, like for instance, in most model-based decompositions. As soils are predominantly rough in agriculture, the classical Rank 1 dihedral scattering component has to be extended to account for soil roughness-induced depolarization. Therefore, an azimuthal ...

Abstract We prove that the number of irreducible real characters in a nilpotent block finite group is locally determined. further conjecture Frobenius–Schur indicators those can be computed for $$p=2$$ p = 2 terms extended defect group. derive this from...

In this study, we define hyperbolic-type k-Fibonacci numbers and then give the relationships between k-step Fibonacci numbers. addition, study sequence modulo m periods of Hperbolic-type sequences for any k which are related m. Furthermore, extend to groups. Finally, obtain 2-Fibonacci in dihedral group D2m, (m ? 2) with respect generating pairs (x,y) (y, x).

in this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.