catena-Poly[[sodium-di-μ-β-d-glucose] chloride]

The asymmetric unit of the title compound, {[Na(C6H12O6)2]Cl}n, contains six glucose mol­ecules, three Na+ ions and three Cl− ions, i.e. three independent {[Na(C6H12O6)2]Cl} units. Each of these units forms polymeric chains along the c axis. Each Na+ ion is surrounded by six O atoms from four glucose mol­ecules, forming a distorted octa­hedral geometry. All glucose mol­ecules adopt chair conformations. The constituent units are linked into a three-dimensional framework by O—H⋯Cl and O—H⋯O hydrogen bonds, utilizing all the O—H groups

2-[(E)-(2,4,6-Trichloro­phen­yl)imino­meth­yl]phenol

The title mol­ecule, C13H8Cl3NO, exists in a trans configuration with respect to the C=N bond [1.278 (2) Å]. The benzene rings form a dihedral angle of 24.64 (11)°. The mol­ecular structure is stabilized by an intra­molecular O—H⋯N hydrogen bond, which generates an S(6) ring motif. In the crystal, π–π stacking inter­actions [centroid–centroid distances = 3.6893 (14) Å] are observed

2-[(E)-(2,4-Dimethyl­phen­yl)imino­meth­yl]phenol

The asymmetric unit of the title compound, C15H15NO, contains two independent mol­ecules, both of which exist in trans configurations with respect to the C=N bonds [1.278 (2) and 1.279 (2) Å]. In each mol­ecule, intra­molecular O—H⋯N hydrogen bonds generate S(6) ring motifs. In one mol­ecule, the benzene rings form a dihedral angle of 13.38 (9)°, while in the other mol­ecule the dihedral angle is 30.60 (10)°. In the crystal, the two independent mol­ecules are linked via weak inter­molecular C—H⋯O hydrogen bonds

A counterexample on the completion of preferences with single crossing differences

We provide an example of a data set where all the revealed preference relations seem to be consistent with single crossing differences and yet the revealed preference relations cannot be extended to a complete preference obeying that propert

A counterexample on the completion of preferences with single crossing differences

We provide an example of a data set where all the revealed preference relations seem to be consistent with single crossing differences and yet the revealed preference relations cannot be extended to a complete preference obeying that propert

1-[3-(4-Chloro­phen­yl)-5-(4-meth­oxy­phen­yl)-4,5-dihydro-1H-pyrazol-1-yl]butan-1-one

In the title compound, C20H21ClN2O2, the benzene rings form dihedral angles of 6.35 (5) and 81.82 (5)° with the mean plane of the 4,5-dihydro-1H-pyrazole ring (r.m.s. deviation = 0.145 Å). This latter ring adopts an envelope conformation with the CH grouping as the flap. The dihedral angle between the benzene rings is 75.63 (4)°. In the crystal, mol­ecules are linked by C—H⋯Cl and C—H⋯O hydrogen bonds into chains along [-201]. The crystal structure also features C—H⋯π inter­actions

N-(2,6-Dichloro­phen­yl)-2-(naphthalen-1-yl)acetamide

In the title compound, C18H13Cl2NO, the naphthalene ring system and the benzene ring form dihedral angles of 74.73 (13) and 62.53 (16)°, respectively, with the acetamide grouping [maximum deviation = 0.005 (3) Å]. The naphthalene ring system forms a dihedral angle of 75.14 (13)° with the benzene ring. In the crystal, mol­ecules are linked by N—H⋯O hydrogen bonds, forming C(4) chains propagating in [010]. The O atom also accepts two C—H⋯O inter­actions

1-[5-(4-Chloro­phen­yl)-3-(4-hy­droxy­phen­yl)-4,5-dihydro-1H-pyrazol-1-yl]­ethanone

In the title compound, C17H15ClN2O2, the benzene rings form dihedral angles of 89.56 (5) and 5.87 (5)° with the mean plane of the pyrazoline ring (r.m.s. deviation = 0.084 Å). The dihedral angle between the two benzene rings is 87.57 (5)°. In the crystal, mol­ecules are linked by O—H⋯O and C—H⋯O hydrogen bonds into a helical chain along the c axis. Between the chains weak C—H⋯N and C—H⋯O inter­actions are present. The crystal studied was an inversion twin with a domain ratio of 0.72 (4):0.28 (4)

Three closely related (2E,200E)-3,300-(1,4-phenylene)- bis[1-(methoxyphenyl)prop-2-en-1-ones]: supramolecular assemblies in one dimension mediated by hydrogen bonding and C—Hp interactions

In the title compounds, (2E,20E)-3,30-(1,4-phenylene)bis[1-(2-methoxyphenyl)- prop-2-en-1-one], C26H22O4 (I), (2E,20E)-3,30-(1,4-phenylene)bis[1-(3-methoxyphenyl) prop-2-en-1-one], C26H22O4 (II) and (2E,20E)-3,30-(1,4-phenylene)bis[1- (3,4-dimethoxyphenyl)prop-2-en-1-one], C28H26O6 (III), the asymmetric unit consists of a half-molecule, completed by crystallographic inversion symmetry. The dihedral angles between the central and terminal benzene rings are 56.98 (8), 7.74 (7) and 7.73 (7) for (I), (II) and (III), respectively. In the crystal of (I), molecules are linked by pairs of C—H interactions into chains running parallel to [101]. The packing for (II) and (III), features inversion dimers linked by pairs of C—HO hydrogen bonds, forming R2 2(16) and R2 2(14) ring motifs, respectively, as parts of [201] and [101] chains, respectively