The asymmetric unit of the title compound, C(19)H(18)N(2)O(3), comprises a whole organic dipyridinone mol-ecule plus a water mol-ecule of crystallization. The planes of the pyridinone rings are approximately perpendicular with the plane of the central aromatic ring [dihedral angles = 80.68 (8) and 83.65 (8)°]. The C-O bond of the hy-droxy group subtends an angle of 31.71 (10)° with the plane th...

A central problem for psychology is vision's reaction to perspective. In the present studies, observers looked at perspective pictures projected by square tiles on a ground plane. They judged the tile dimensions while positioned at the correct distance, farther or nearer. In some pictures, many tiles appeared too short to be squares, many too long, and many just right. The judgments were strong...

In the title compound, C(29)H(19)F(2)NO(2), the central benzene ring forms a dihedral angle of 56.92 (12)° with the cyano-benzene ring and dihedral angles of 40.91 (12) and 44.76 (12)° with the two fluoro-benzene rings. In the crystal, C-H⋯O and C-H⋯F hydrogen bonds link the mol-ecules into sheets lying parallel to the ab plane. The crystal packing also features C-H⋯π inter-actions involving th...

In the title compound, C(24)H(22)O(4), the centroid of the central benzene ring lies on a special position of 2/m site symmetry, while the terminal aromatic rings are located on a mirror plane. The central and terminal benzene rings are perpendic-ular to each other. In the crystal, the mol-ecules are connected via C-H⋯O hydrogen bonds into a three-dimensional polymeric structure. The network is...

The complete mol-ecule of the title compound, C(20)H(19)NO(5)S(2), is generated by a crystallographic twofold axis and the O atom and N-H group attached to the central benzene ring are statistically disordered. The dihedral angle between the central and terminal benzene rings is 56.91 (5)° and that between the terminal benzene rings is 29.80 (5)°. In the crystal, N-H⋯O hydrogen bonding links th...

The polynomial α=xy∏i=3m(aix+y)∈C[x,y] determines a plane central line arrangement α = 0. We compute explicitly multivariate Bernstein–Sato ideals of α by using the decomposition behavior D2...

This paper deals with the basic notions of k-tautimmersions . These notions come from two special cases; that is, tight and taut immersions. Tight and taut based on high and distance functions respectively and their basic notions are normal bundle, endpoint map, focal point, critical normal. We generalize hight and distance functions to cylindrical function and define basic notions of k-taut ...

Differential diagnosis between peripheral and central spontaneous nystagmus can be difficult to classify (as peripheral or central) even on the basis of criteria recommended in the recent literature. The aim of this paper is to use the combination of spontaneous nystagmus and ocular tilt reaction to determine the site of origin of the disease that causes nystagmus. We propose to classify the ny...