In the title compound, C14H8ClNO5, the benzene rings form a dihedral angle of 19.55 (9)°. The mean plane of the central ester group [r.m.s. deviation = 0.024 Å] forms dihedral angles of 53.28 (13) and 36.93 (16)°, respectively, with the nitro- and chloro-substituted rings. The nitro group forms a dihedral angle of 19.24 (19)° with the benzene ring to which it is attached. In the crystal, mol-ec...

This paper investigates a connection between self-similar group representations and induced rational maps on the projective space which preserve spectrum of group. The focus is infinite dihedral D?. main theorem states that Julia set map F P2 for D? union with F's extended indeterminacy set. Moreover, limit function iteration sequence {F?n} Fatou fully described. discovery finds an application ...

In the imidazo[2,1-b][1,3]thia-zole group of the title compound, C(21)H(17)ClN(4)O(2)S, the dihedral angle between the thia-zole and imidazole rings is 1.9 (2)°. The mean plane of this group makes dihedral angles of 5.5 (2) and 39.9 (2)° with the benzene rings of the chloro-phenyl and meth-oxy-phenyl groups, respectively. The dihedral angle between these two benzene rings is 34.4 (2)°. In the c...

In the title compound, C(31)H(29)NO(5), the methyl carboxyl-ate and dimethyl-amino groups on the naphtho-pyran group are almost coplanar with the naphtho-pyran ring system [r.m.s. deviations = 0.08 (2) and 0.161 (2) Å, respectively]. The dihedral angle between the methyl carboxyl-ate and dimethyl-amino groups is 4.9 (1)°. The pyran ring has an envelope conformation with the quaternary C atom ou...

In the title compound, C(23)H(26)N(2)O(2)S, the sulfur-bound phenyl group is aligned approximately parallel to one of the two rings of the benzhydryl group, making a dihedral angle of 1.15 (9)°. The other forms a dihedral angle of 59.20 (9)° with the phenyl group bound to the S atom. In the crystal, mol-ecules are linked into strands along [100] by weak C-H⋯O contacts. Weak C-H⋯π inter-actions ...

We consider the kernel of the natural projection from the Artin group of dihedral type I2(k) to the associated Coxeter group, which we call a pure Artin group of dihedral type and write PI2(k). We show that the growth rates for both the spherical growth series and geodesic growth series of PI2(k) with respect to a natural generating set are Pisot numbers. 2010 Mathematics Subject Classification...

In the title compound, C(17)H(23)NO(4)S, the penta-diene group adopts a planar conformation, with an r.m.s. deviation of 0.0410 (14) Å. The phenyl ring makes a dihedral angle of 85.73 (11)° with the penta-diene group, while the penta-diene group makes dihedral angles of 11.38 (11) and 14.08 (10)°, respectively, with the amino and ester groups. In the crystal, molecules are linked via pairs of C...

In the title compound, C(17)H(15)Cl(2)NO, the dimethyl-amino-phenyl group is close to coplanar with the central propenone group [dihedral angle = 13.1 (1)° between the mean planes], while the dichloro-phenyl group is twisted from the plane [dihedral angle = 64.0 (1)°]. In the crystal, C-H⋯O and weak C-H⋯π inter-actions are formed between mol-ecules.

In the title compound, C17H16O4, the dihedral angle between the benzene rings is 21.22 (1)° and the mean plane of the prop-2-en-1-one group makes dihedral angles of 10.60 (1) and 11.28 (1)°, respectively, with those of the hy-droxy-phenyl and eth-oxy-phenyl rings. The eth-oxy substituent forms a dihedral angle of 88.79 (2)° with the the prop-2-en-1-one group, which is found to be slightly twist...