In the title compound, C(21)H(30)N(2)O(5)S, the plane of the dimeth-yl-thio-carbamic group makes a dihedral angle of 78.41 (7)° with the central benzene ring. One of the carbonyl groups in the α,β-unsaturated malonate side chain makes a dihedral angle of 8.73 (10)° with the central benzene ring, while the other carbonyl group makes a dihedral angle of 81.52 (8)°.

In the title mol-ecule, C(17)H(14)ClFN(2)O, the mean plane of the pyrazoline ring makes dihedral angles of 18.19 (1) and 83.51 (4)° with the 4-chloro-benzene and 4-fluoro-benzene rings, respectively. The two benzene rings make a dihedral angle of 76.11 (2)°. Weak inter-molecular C-H⋯O hydrogen bonds help stabilize the crystal structure.

In the title compound, C15H12FN3O, the triazole ring forms dihedral angles of 30.57 (8) and 21.81 (9)° with the fluoro-substituted and meth-oxy-substituted benzene rings, respectively. The dihedral angle between the benzene rings is 51.53 (7)°. In the crystal, π-π inter-actions between the triazole rings [centroid-centroid seperations = 3.774 (2) and 3.841 (2) Å] form chains along [010].

In the title compound, C(15)H(14)N(2)O(2), the aromatic rings are oriented at a dihedral angle of 24.52 (5)°. The dihedral angle between the nitro group and its parent benzene ring is 9.22 (16)°. In the crystal, mol-ecules inter-act through aromatic π-π stacking inter-actions [centroid-centroid separations = 3.8158 (14) and 3.9139 (14) Å].

R. S. Kulkarni showed that a finite group acting pseudofreely, but not freely, preserving orientation, on an even-dimensional sphere (or suitable sphere-like space) is either a periodic group acting semifreely with two fixed points, a dihedral group acting with three singular orbits, or one of the polyhedral groups, occurring only in dimension 2. It is shown here that the dihedral group does no...

In the title compound, C13H7Cl3O2, the dihedral angle between the benzene rings is 82.1 (2)°. The dihedral angle between the CO2 group and its carbon-bonded ring is 14.50 (19)° In the crystal, aromatic π-π stacking inter-actions [minimum ring centroid separation = 3.604 (2) Å] occur.

In the title compound C(11)H(9)Cl(2)NO(2), the dihedral angle between the benzene and cyclo-propane ring planes is 89.95 (13)°. The carbon-yl-oxime grouping is almost coplanar with the benzene ring [dihedral angle = 4.08 (6)°]. In the crystal, mol-ecules are linked by C-H⋯O inter-actions into [100] chains.

We present algorithms for constructing and tabulating degree-` dihedral extensions of Fq(x), where q ≡ 1 mod 2`. We begin with a Kummertheoretic algorithm for constructing these function fields with prescribed ramification and fixed quadratic resolvent field. This algorithm is based on the proof of our main theorem, which gives an exact count for such fields. We then use this construction metho...

The title compound, C42H48O6, was obtained via formyl-ation of 25,26,27,28-tetra-propoxycalix[4]arene with dichloro-methyl methyl ether and tin tetra-chloride. It adopts a pinched cone conformation, which leads to an open cavity. The two opposite aromatic rings bearing formyl groups are almost parallel, making a dihedral angle of 29.1 (2)°. The other pair of opposite rings are close to being pe...

In the title compound, C24H17BrFN3S, the pyrazole ring is almost planar (r.m.s. deviation = 0.043 Å), with all but the perpendicular fluoro-benzene ring substituents [dihedral angle = 77.9 (3)°] being very approximately coplanar [dihedral angle with the 2-thienyl ring = 19.4 (3)° and with the bromo-benzene ring = 20.3 (3)°; dihedral angle between the 2-thienyl and attached phenyl ring = 11.0 (4...