The asymmetric unit of the title compound, C(13)H(10)F(2)N(2)O, contains one and a half N,N'-bis-(4-fluoro-phen-yl)urea mol-ecules. One of the mol-ecules has crystallographic twofold rotation symmetry. The benzene rings are twisted from each other by dihedral angles of 29.69 (6)° for the mol-ecule in a general position and 89.83 (6)° for the symmetry-generated mol-ecule. In the crystal structur...

We compute the number of rhombus tilings of a hexagon with sides N, M, N, N, M, N , which contain a fixed rhombus on the symmetry axis that cuts through the sides of length M .

The exact metric around a wiggly cosmic string is found by modifying the energy momentum-tensor of a straight infinitely thin cosmic string to include an electric current along the symmetry axis.

We prove the existence of many different symmetry types of relative equilibria for systems of identical point vortices on a non-rotating sphere. The proofs use the rotational symmetry group SO(3) and the resulting conservation laws, the time-reversing reflectional symmetries in O(3), and the finite symmetry group of permutations of identical vortices. Results include both global existence theor...

The Symmetry Set (SS) and its representation in parameter space, the pre-Symmetry Set, can be used to describe a shape with a linear data structure containing strings. As shape descriptor one specific string can be chosen. This string represents not only the major axis of the shape, but it also contains information of the complete shape. The string is augmented with information about the specia...

This communication reports an asymmetric charge transport with a large rectification ratio and finely featured NDR (negative differential resistance) by d-orbitals of a neutral ruthenium(ii) complex with a C(2) axis of symmetry.

When all planes transverse and nearly perpendicular to the axis of a surface of revolution S intersect it in loops having central symmetry, S must be quadric. Dedicated to Sue Swartz

We prove that the angular velocity equations can be smoothly stabilized with a single torque controller for bodies having an axis of symmetry. This complements a recent result of Aeyels and Szafranski.

The mol-ecule of the title compound, C19H15N3O2, is completed by the application of crystallographic twofold symmetry, with the pyridine N atom lying on the rotation axis. The mol-ecular structure is approximately planar, the dihedral angle between the mean planes of the pyridine and benzene rings being 7.53 (11)°. In the crystal, N-H⋯O hydrogen bonds link the mol-ecules into a two-dimensional ...

In the title compound, C(14)H(12)ClNO·0.5H(2)O, the water mol-ecule is located on a twofold axis of symmetry. The meta-Cl atom in the aniline ring is positioned anti to the N-H bond. The two benzene rings make a dihedral angle of 40.40 (11)°. The crystal structure is stabilized by inter-molecular N-H⋯O and O-H⋯O hydrogen bonds, which link the mol-ecules into chains along the a axis.