In the mol-ecule of the title compound, C(15)H(13)Cl(2)N(3)O(2), the triazole ring is oriented at dihedral angles of 14.8 (2) and 81.5 (1)° to the furan and dichloro-benzene rings, respectively. The dihedral angle between the dichloro-benzene and furan rings is 86.3 (2)°. An intra-molecular C-H⋯O hydrogen bond results in the formation of a planar [maximum deviation 0.012 (2) Å] five-membered ri...

Classic convolutional codes are defined as the convolution of a message and a transfer function over Z. In this paper, we study convolutional codes over the infinite dihedral group D∞. The goal of this study is to design convolutional codes with good and interesting properties and intended to be more resistant to code recognition. Convolution of two functions on D∞ corresponds to the product of...

This research is about the group coverings of subsets finite non-abelian groups and its application in field cryptography. Group abelian has been researched over years it many applications various fields. The popularity internet increased rapidly cryptography become more important as ensures privacy security users network. A cryptosystem a structure consisting several cryptographic primitives. ...

The title compound, C(14)H(15)BrO(2), contains a sterically unencumbered norbornyl group. The dihedral angle between the plane of the carboxyl-ate group and the mean plane of the adjacent benzene ring is 5.3 (2)°. The dihedral angle between the plane of the carboxyl-ate group and the norbornyl methano C-O bond is 4.5 (1)°, the methano C atom deviating by 0.141 (2) Å from this plane. In the crys...

in this paper we define s algebras and show that every finite group can be found in some s algebra.  we define and study the s degree of a finite group and determine the s degree of several classes of finite groups such as cyclic groups, elementary abelian $p$-groups, and dihedral groups $d_p$.

The main result of this article is a classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious families of such graphs, which are called trivial. These are: complete graphs, complete bipartite graphs, complete bipartite graphs with the edges of a 1-factor removed, and cycles. It is proved that every nontrivial distance-regular Cayley graph on a dihedral group...

In the title compound, C(16)H(11)ClN(2)O(2), the pyrazole ring makes dihedral angles of 11.88 (13) and 22.33 (13)° with the 3-chloro-2-hy-droxy-benzene group and phenyl rings, respectively. The phenolic hy-droxy group forms an intra-molecular O-H⋯N hydrogen bond with the imine N atom of the pyrazole unit. The formyl group is virtually coplanar with the pyrazole ring [dihedral angle = 4.5 (19)°]...

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, C(15)H(14)N(2)O(2), the aromatic rings are oriented at a dihedral angle of 24.52 (5)°. The dihedral angle between the nitro group and its parent benzene ring is 9.22 (16)°. In the crystal, mol-ecules inter-act through aromatic π-π stacking inter-actions [centroid-centroid separations = 3.8158 (14) and 3.9139 (14) Å].