The asymmetric unit of the title salt solvate, C(17)H(17)F(6)N(2)O(+)·C(7)H(5)N(2)O(4) (-)·1.5H(2)O, comprises a piperidin-1-ium cation, a 3-amino-5-nitro-benzoate anion, and three fractionally occupied [i.e. 0.414 (3), 0.627 (6) and 0.459 (5)] disordered water mol-ecules of solvation. The cation has an L shape with a C-C-C-C torsion angle of -102.9 (3)° for the atoms linking the quinolinyl gro...

There are two independent mol-ecules in the asymmetric unit of the title compound, C13H13NO5S, in both of which the ester substituent is nearly coplanar [C-C-C-O torsion angles = 2.7 (7) and -0.8 (7)°] with the planar fragment of the bicycle due to the formation of a strong O-H⋯O intra-molecular hydrogen bond. The vinyl group at the ring N atom is approximately orthogonal to the heterocyclic me...

Large size effects are experimentally measured in lattices of triangular unit cells: about a factor of 36 in torsion rigidity and 29 in bending rigidity. This nonclassical phenomenon is consistent with Cosserat elasticity, which allows for the rotation of points and distributed moments in addition to the translation of points and force stress of classical elasticity. The Cosserat characteristic...

The mol-ecular structure of the title compound, C(26)H(32)N(3)S(+)·PF(6) (-), shows a protonated guanidyl group bridged by an ethyl-ene linker with a tritylsulfanyl unit. The guanidinium (gua) unit displays charge delocalization over the three N-C(gua) bonds. The N-C-C-S group shows a folded nonplanar conformation with a torsion angle of 158.4 (1)°. In the crystal, the cation and anion are link...

Background: Left ventricular torsion is one of the most important biomechanical parameters of heart that routinely is measured in short axis view.  A review of the literature has indicated that assessment of left ventricular torsion in short axis view has some limitations. In the present study, we evaluated whether torsion angle assessment in long axis view can be used as a diagnostic biomechan...

In the present paper a geometrization of electrodynamics is proposed, which makes use of a generalization of Riemannian geometry considered already by Einstein and Cartan in the 20ies. Cartan’s differential forms description of a teleparallel space–time with torsion is modified by introducing distortion 1-forms which correspond to the distortion tensor in dislocation theory. Under the condition...

We study the effect of twist on the electronic structure of H-terminated armchair graphene nanoribbons, for both relaxed and unrelaxed unit cell size. We investigate the band gap change as a function of the twist angle for different ribbon widths. In the case of unrelaxed unit cell size, the band gap closes for smaller twist angles as opposed to relaxed unit cell size. We calculate strain energ...

The title compound, C(10)H(10)Cl(2)N(2)O(2), features a planar C(ar)-N(H)-N=C(Cl) unit [torsion angle = 5.5 (4)°] whose benzene substituent is coplanar with it [dihedral angle = 4.7 (4)°]; this unit is slightly twisted with respect to the carboxyl -CO(2) fragment [dihedral angle = 2.2 (52)°]. The amino group acts as a hydrogen-bond donor to the carbonyl O atom of an adjacent mol-ecule; the hydr...

The title compound, C(10)H(11)ClN(2)O(2), features an almost planar C(ar)-N(H)-N=C(Cl) unit [torsion angle = 0.8 (1)° whose phenyl substituent is almost coplanar with it [dihedral angle = 2.8 (2)°]; this unit is slightly twisted with respect to the carboxyl -CO(2) fragment [dihedral angle = 10.3 (2)°]. In the crystal, the amino group acts as a hydrogen-bond donor to the carbonyl O atom of an ad...

We develop an algorithm for bounding the rank of elliptic curves in the family y2 = x3−B x, all of them with torsion group Z/(2Z) and modular invariant j = 1728. We use it to look for curves of high rank in this family and present four such curves of rank 13 and 22 of rank 12.