In the title compound, C(17)H(10)F(6)N(4)O(2)S, an intra-molecular N-H⋯N hydrogen bonds forms an S(5) ring whereas N-H⋯O and C-H⋯S inter-actions complete S(6) ring motifs. The dihedral angle between the fused ring system and the phenyl ring is 6.68 (8)°. In the crystal, the mol-ecules are dimerized due to N-H⋯O inter-actions. π-π inter-actions are present between the benzene rings [centroid-cen...

In the title compound, C(17)H(17)NO(3)S, the cyclohexene ring is essentially planar, with a maximum deviation of 0.006 (1) Å. The cyclo-hexene ring adopts a half-chair conformation. The dihedral angle between the thio-phene and benzene rings is 29.7 (1)°. The mol-ecular structure exhibits intra-molecular O-H⋯O, O-H⋯N and C-H⋯S hydrogen bonds, which generate one S(5) and two S(6) motifs. There i...

The title compound, C(17)H(16)N(4)OS, is stabilized in the form of a two-dimensional polymeric network due to inter-molecular N-H⋯S and N-H⋯O hydrogen bonds. An intra-molecular N-H⋯N hydrogen bond forms an S(5) ring, whereas inter-actions of the N-H⋯O and C-H⋯S types complete S(6) ring motifs. π-π inter-actions with a centroid-centroid distance of 3.6514 (10) Å are found between the ethyl-subst...

In the title compound, C(15)H(10)FN(5)O(3)S, an intra-molecular N-H⋯N hydrogen bond generates an S(5) ring, whereas N-H⋯O and C-H⋯S inter-actions complete S(6) ring motifs. The dihedral angle between the isatin ring system and the fluoro-benzene ring is 5.96 (6)° and the complete mol-ecule is close to planar (r.m.s. deviation for all the non-H atoms = 0.112 Å). In the crystal, mol-ecules are li...

In the title mol-ecule, C(16)H(16)O(4)S, the enone fragment, thio-phene ring and benzene ring are individually essentially planar. The thio-phene ring is disordered over two sites, corresponding to a rotation of approximately 180° about the single C-C bond to which it is attached. The approximate ratio of occupancies for the major and minor components is 0.872 (2):0.128 (2). The major component...

In the title mol-ecule, C(9)H(6)BrN(3)OS(2), the dihedral angle between the benzene ring and the five-membered ring is 5.5 (3)°. An intra-molecular O-H⋯N hydrogen bond forms an S(6) ring motif. In the crystal, N-H⋯S hydrogen bonds link mol-ecules into centrosymmetric dimers creating R(2) (2)(8) ring motifs. In addition, there are inter-molecular S⋯S [3.430 (2) Å] contacts. The crystal used was ...

In this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. Weobserve that over a commutative ring $R$, $Bbb{AG}_*(_RM)$ isconnected and diam$Bbb{AG}_*(_RM)leq 3$. Moreover, if $Bbb{AG}_*(_RM)$ contains a cycle, then $mbox{gr}Bbb{AG}_*(_RM)leq 4$. Also for an $R$-module $M$ with$Bbb{A}_*(M)neq S(M)setminus {0}$, $...

In the title compound, C(25)H(22)BrN(3)O(5)S, the central benzene ring makes dihedral angles of 32.02 (14), 37.49 (18) and 80.52 (13)°, respectively, with the pyrazolone ring, the bromo-benzene ring and the terminal phenyl ring. This conformation features a short intramolecular C-H⋯O contact that generates an S(6) ring. In the crystal, inversion dimers linked by pairs of C-H⋯O=C hydrogen bonds ...

‎A recent result due to Ha and Van Tuyl proved that the Castelnuovo-Mumford regularity of the quotient ring $R/I(G)$ is at most matching number of $G$‎, ‎denoted by match$(G)$‎. ‎In this paper‎, ‎we provide a generalization of this result for powers of edge ideals‎. ‎More precisely‎, ‎we show that for every graph $G$ and every $sgeq 1$‎, ‎$${rm reg}( R‎/ ‎I(G)^{s})leq (2s-1) |E(G)|^{s-1} {rm ma...

In the title compound, C(17)H(18)N(2)O(2)S, the 1,3-diazinane-2-thione ring system is not coplanar with the benzene ring and meth-oxy-phenyl ring system, the dihedral angle between the planes being 65.58 (13) and 89.18 (10)°, respectively. The crystal structure is characterized by inter-molecular O-H⋯S, N-H⋯S, N-H⋯O and C-H⋯S hydrogen bonding.