2,2′-(Piperazine-1,4-diyl)diacetonitrile

Julian Sorell Huxley 22 June 1887- 14 February 1975.

# a 22 Integers 14 ( 2014 ) a Density Chinese Remainder Theorem

Given collections A and B of residue classes modulo m and n, respectively, we investigate conditions on A and B that ensure that, for at least some (a, b) 2 A⇥B, the system: x ⌘ a mod m and x ⌘ b mod n has an integer solution, and we quantify the number of such admissible pairs (a, b). The special case where A and B consist of intervals of residue classes has application to the Lonely Runner Co...

12β,14-Dihy­droxy-3-oxo-5β,20(22)-cardenolide monohydrate

The title compound, digoxigenone, C(23)H(30)O(5)·H(2)O, was biotransformed from digoxigenin. In the crystal, inter-molecular O-H⋯O hydrogen bonds contribute to the formation of a three-dimensional supra-molecular structure. The title compound has three fused six-membered rings (A,B,C) and two non-fused five-membered rings (D,E). As in other structures, compound nucleus has a cis-trans-cis confo...

Piperazine-1,4-diium diacetate

In the title salt, C(4)H(12)N(2) (2+)·2C(2)H(3)O(2) (-), the piperazine-1,4-diium cation has 2/m symmetry with the NH(2) unit located on a mirror plane and the acetate anion has m symmetry with all non-H atoms and one H atom located on a mirror plane. The piperazine ring adopts a chair conformation. In the crystal, the cations are linked with the anions via N-H⋯O hydrogen bonding into chains pa...

Tetra­phenyl piperazine-1,4-diyldiphos­pho­nate

The mol-ecule of the title compound, C(28)H(28)N(2)O(6)P(2), is organized around an inversion center located at the centre of the piperazine ring. Both piperazine N atoms are substituted by P(O)(OC(6)H(5))(2) phospho-ester groups. The P atoms display a slightly distorted tetra-hedral environment; the N atoms show some deviation from planarity. The O atoms of the P=O groups are involved in inter...