In the title compound, C(24)H(16)O(2), the naphthalene ring system makes dihedral angles of 78.5 (6) and 65.5 (7)° with the terminal and central benzene rings, respectively. The dihedral angle between the benzene rings is 74.5 (8)°. In the crystal, neighbouring molecules are interlinked through two C-H⋯π interactions, which construct a two-dimensional supramolecular framework extending infinite...

Forcing polymers to be semiconductors In mechanochemistry, the application of force to a polymer is used to pry open specific chemical bonds. Chen et al. leveraged this technique to produce semiconducting blocks of polyacetylene in an insulating precursor. Ring-opening metathesis polymerization tethered together a series of fused fourcarbon rings, reminiscent of the unusual ladderane membrane l...

The title compound, C(15)H(16)O(2), has a dihedral angle of 19.10 (5)° between the mean planes of the two benzene rings. There is an intra-molecular O-H⋯O hydrogen bond and the C-C-C-C torsion angle across the bridge between the two rings is 173.13 (14)°. The mol-ecules form inter-molecular O-H⋯O hydrogen-bonded chains extending along the a axis. C-H⋯π contacts are also observed between mol-ecu...

In the title compound, C(15)H(15)N(5)O(4)S(2), the dihedral angles between the central 1,2,4-triazole ring and the pendant benzene rings are 55.61 (10) and 68.59 (10)°; the dihedral angle between the benzene rings is 63.66 (9)°. Intra-molecular N-H⋯N and N-H⋯O hydrogen bonds generate S(7) and S(12) rings, respectively. In the crystal, sheets extending in the (101) plane arise, with the mol-ecul...

In the title compound, C12H11NO, the pyridine and phenyl rings are inclined to each other by 71.42 (10)°. In the crystal, O-H⋯N hydrogen bonds link the mol-ecules into helical chains extending along the c-axis direction.

In the title salt, C21H29N2O(+)·Cl(-), the benzene rings form a dihedral angle of 6.13 (1)°. In the crystal, N-H⋯Cl hydrogen bonds link the cations and anions into chains extending along the c axis.

in this paper we focus on a special class of commutative local‎ ‎rings called spap-rings and study the relationship between this‎ ‎class and other classes of rings‎. ‎we characterize the structure of‎ ‎modules and especially‎, ‎the prime submodules of free modules over‎ ‎an spap-ring and derive some basic properties‎. ‎then we answer the‎ ‎question of lam and reyes about strongly oka ideals fam...

3 Derived Categories 11 3.1 Extending Functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 Truncations and Hearts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.3 Bounded Derived Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4 Plump Subcategories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

In this paper, we introduce a dimension, called the cotorsion dimension, for modules and rings. The relations between the cotorsion dimension and other dimensions are discussed. Various results are developed, some extending known results.

In the title compound, C18H18O4, the planes of the benzene rings are twisted by 81.60 (5)°. In the crystal, weak C-H⋯O hydrogen bonds link the mol-ecules into supra-molecular chains extending along the a axis.