The title Schiff base, C(24)H(21)N(3)O(2), adopts an E configuration with respect to the central C=N bond. The pyrazole ring and the central benzene ring attached to the imino group are almost coplanar. The phenyl ring attached to the pyrazole unit is twisted by 39.3 (2)° with respect to the pyrazole ring plane. The phen-oxy benzene ring makes a dihedral angle of 79.8 (2)° with the central benz...

In the title compound, [Ni(H(2)O)(6)](C(16)H(12)O(6))·H(2)O, the Ni(II) cation is located on a mirror plane and is coordinated by six water mol-ecules, two of which are also located on the mirror plane, in a distorted octa-hedral geometry. The 4,4'-(1,2-dihy-droxy-ethane-1,2-di-yl)dibenzoate anion is centrosymmetric with the mid-point of the central ethane C-C bond located on an inversion cente...

The central problem of the total-colorings is the total-coloring conjecture, which asserts that every graph of maximum degree ∆ admits a (∆+2)-total-coloring. Similar to edge-colorings—with Vizing’s edge-coloring conjecture—this bound can be decreased by 1 for plane graphs of higher maximum degree. More precisely, it is known that if ∆ ≥ 10, then every plane graph of maximum degree ∆ is (∆ + 1)...

The piperidone ring in the title compound, C(20)H(23)NO(3)S(2), has a distorted half-chair conformation with the central methyl-ene atom of the propyl fragment lying 0.696 (1) Å out of the plane defined by the other five atoms (r.m.s. deviation = 0.071 Å). One of the S-bound phenyl rings is almost perpendicular to the mean plane through the piperidone ring, whereas the other is splayed [dihedra...

In the title compound, C(21)H(19)BrO(2), the dihedral angles between the central benzene ring and the two peripheral rings are 50.28 (5) and 69.75 (2)°. The O-CH(2) bonds lie in the plane of the central ring and adopt a syn-anti conformation.

The title compound, C(32)H(24)N(6)O(2), has an inversion centre located at the mid-point of the central C-C bond of the diether bridging unit. The terminal pyridine rings are canted relative to the central pyridine ring, with dihedral angles of 12.98 (6) and 26.80 (6)°. The maximum deviation from the eight-atom mean plane, defined by the two bridging O and C atoms and the central pyridine ring,...

The central problem of the total-colourings is the Total-Colouring Conjecture, which asserts that every graph of maximum degree ∆ admits a (∆ + 2)-total-colouring. Similarly to edge-colourings—with Vizing’s edge-colouring conjecture—this bound can be decreased by 1 for plane graphs of higher maximum degree. More precisely, it is known that if ∆ ≥ 10 then every plane graph of maximum degree ∆ is...

Moire photographs of the lingual surfaces of eight upper central incisors were taken using a specially designed standard plane. This plane was formed by three points, namely the most protruding points of the lingual tubercle, and the mesial and distal marginal ridges of the lingual surface. When the moire photographs taken using this standard plane were observed, they showed a high reproducibil...

The title compound, C(28)H(38)Br(2)N(2), is centrosymmetric with the mid-point of the central C-C bond of the butyl group located on an inversion center. The terminal benzene ring is approximately perpendicular to the central 1,4-diaza-butadiene mean plane [dihedral angle = 78.23 (3)°]. No hydrogen bonding or aromatic stacking is observed in the crystal structure.

A central problem in the field of geometric algorithms is to compare algorithms that process vector-type data specified in the continuous plane with algorithms that process raster-type data specified in the digitized plane. A set of criteria is proposed that a digitization of a collection of line segments should satisfy in order to be said to represent the same structure as their continuous pla...