We develop general results on centroids of Lie algebras and apply them to determine the centroid of extended affine Lie algebras, loop-like and Kac-Moody Lie algebras, and Lie algebras graded by finite root systems.

In the title compound, C(12)H(16)N(2)O, the dihedral angle between the pyridine ring and C/O/N plane is 22.93 (7)°. In the crystal structure, inter-molecular N-H⋯O hydrogen bonds link the mol-ecules, forming extended chains along [001]. π-π inter-actions between inversion-related pyridine rings [centroid-centroid distance = 3.825 (2)Å] are also observed.

In the title mol-ecular salt, C18H22NO(+)·C7H7O3S(-), the dihedral angle between the aromatic rings in the cation is 10.00 (9)°; its alkyl side chain adopts an extended conformation. In the crystal, weak C-H⋯O and π-π [centroid-centroid distance = 3.7658 (17) Å] inter-actions link the components, generating a three-dimensional network.

The title compound, C12H9N3, is an unhydrated analogue of the previously reported trihydrate. The mol-ecule is essentially planar, with a 3.62 (11)° angle between the pyridine and benzimidazole planes. In the crystal, N-H⋯N hydrogen bonds result in chains of mol-ecules parallel to [010], which are additionally linked by weak π-π stacking inter-actions [centroid-centroid distance = 3.7469 (17) Å...

The title mononuclear Zn(II) complex, [ZnCl(2)(C(15)H(13)N(5))(2)], is isotypic with the previously reported Hg(II) complex. The Zn(II) atom is located on a twofold rotation axis and has a distorted tetra-hedral environment of two Cl atoms and two N atoms from two heterocyclic ligands. In the crystal, complex mol-ecules are extended by inter-molecular π-π inter-actions [centroid-centroid distan...

The title compound, C(20)H(14)N(2)O(4)·H(2)O, was synthesized by the reaction of fluorescein and hydrazine hydrate in ethanol. In the crystal structure, the organic mol-ecules are linked into extended two-dimensional networks by inter-molecular hydrogen bonding. Additional face-to-face π-π stacking inter-actions between the phenolic benzene rings in two adjacent mol-ecules [centroid-to-centroid...

In the title compound, C(17)H(18)BrClN(2)O, the dihedral angle between the aromatic rings is 3.0 (1)°. The methyl-ethanamine group assumes an extended conformation. An intra-molecular O-H⋯N hydrogen bond generates an S(6) ring motif. The crystal packing is stabilized by C-H⋯π and π-π [centroid-centroid distances = 3.691 (1) and 3.632 (1) Å] inter-actions.

In the title zwitterionic compound, C(16)H(8)N(4)O(4), the dihedral angle between the carboxyl and carboxyl-ate groups is 72.14 (2)°. In the crystal, mol-ecules are linked by strong inter-molecular O-H⋯O(-) and N(+)-H⋯O(-) hydrogen bonds into double chains extended along [001]. These chains are additionally stabilized by π-π stacking inter-actions between the pyridine and benzene rings [centroi...

The present study uses the envelope modulation spectrum (EMS) measure to assess the effect of language, speaking style, and age on rhythm. Three experiments using a weighted mean of the EMS called the spectral centroid were conducted. The first examined rhythm in English and Croatian across conversational and clear speaking styles. The second experiment compared rhythmic characteristics of mono...