In the title compound, C21H21Cl2NO2, the piperidine ring adopts a distorted boat conformation. The phenyl rings substituted at the 2- and 6-positions of the piperidine ring subtend angles of 87.9 (7) and 70.8 (9)°, respectively, with the best plane through the piperidine ring. In the crystal, mol-ecules are connected by C-H⋯O and C-H⋯Cl inter-actions into layers in the ab plane.

A ring signature system is strongly unforgeable if the ring signature is existential unforgeable and, given ring signatures on some message m, the adversary can not produce a new ring signature on m. Strongly unforgeable ring signatures are useful for constructing chosen-ciphertext secure cryptographic system. For example, it can be used to design the ring signcryptionscheme.In this paper, we a...

Let R be an associative ring in which an identity element is not assumed. A right quotient ring of P is an overring 5 such that for each aQS there corresponds rQR such that arQR and ar 9*0. A theorem of R. E. Johnson [l ] states that R possesses a right quotient ring S which is a (von Neumann) regular ring if and only if P has vanishing right singular ideal. In this case P possesses a unique (u...

The title compound, C25H24ClN3, comprises a 2-imino-pyridine ring fused with a cyclo-octane ring, which adopts a twist boat-chair conformation. In the crystal, C-H⋯N inter-actions form R 2 (2)(14) ring motifs and mol-ecules are further connected by weak C-H⋯π inter-actions. The resulting supra-molecular structure is a two-dimensional framework parallel to the ab plane.

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...

The pyran-oside ring in the title compound, C(21)H(24)O(11), has a chair conformation with the substituted benzene ring occupying an equatorial position. The crystal packing is dominated by C-H⋯O inter-actions that lead to the formation of supra-molecular layers in the ab plane.

The title compound, C(19)H(26)O(4), was biotransformed from androstenedione. In the crystal, inter-molecular O-H⋯O hydrogen bonds link molecules into a corrugated sheet, which lies parallel to the ab plane. Ring A has a slightly distorted half-chair conformation, rings B and C adopt chair conformations, while the cyclo-pentane ring D adopts a 14α-envelope conformation.

In the title compound, C19H14FNS2, the seven-membered thia-zepine ring adopts a slightly distorted twist boat conformation. The dihedral angle between the benzene rings is 53.6 (1)°. The mean plane of the thia-zepine ring is twisted by 34.3 (7)° and 36.6 (7)° from the benezene rings. A C-H⋯F interaction generates stacking of molecules along the ab plane.

Fulvene is a non-aromatic molecule, but variation of the electron-donating/withdrawing power of substituents exo to the five-membered ring can drive the system between the extremes of aromatic and antiaromatic, as judged by prediction of fully developed diatropic and paratropic ring currents through ab initio calculations made at the ipsocentric 6-31G**/CTOCD-DZ CHF level.

The galactose ring in the title compound, C(21)H(24)O(11), has a chair conformation with the substituted benzene ring occupying an equatorial position. The crystal packing features C-H⋯O inter-actions that lead to the formation of supra-molecular layers in the ab plane.