2-Phenyl­imidazolium hemi(benzene-1,4-dicarboxyl­ate) trihydrate

The asymmetric unit of the title compound, C9H9N2 +.0.5C8H4O4 −·3H2O, contains one 2-phenyl­imidazolium cation, half a benzene-1,4-dicarboxyl­ate anion and three water mol­ecules, which are connected by O—H⋯O and N—H⋯O hydrogen bonds into a three-dimensional network

catena-Poly[[[bis­[4-(1H-1,3,7,8-tetra­azacyclo­penta­[l]phenanthren-2-yl)phenol-κ2 N 7,N 8]manganese(II)]-μ-naphthalene-1,4-dicarboxyl­ato-κ2 O 1:O 4] naphthalene-1,4-dicarboxylic acid hemisolvate monohydrate]

The 1,4-dicarboxyl­ate dianions in the title compound, [Mn(C12H6O4)(C19H12N4O)2]·0.5C12H8O4·H2O, bond to two 4-(1H-1,3,7,8-tetra­azacyclo­penta­[l]phenanthren-2-yl)phenol-chelated Mn atoms to form a chain that features the metal atom in an octa­hedral coordination geometry. Adjacent chains inter­act with the uncoordinated water mol­ecules to form a three-dimensional network. The naphthalene-1,4-dicarboxylic acid solvent mol­ecule, which is disordered about a centre of inversion, occupies the space within the network but is not bonded to the network. One NH group is disordered equally over two positions

Divergence and Shannon information in genomes

Shannon information (SI) and its special case, divergence, are defined for a DNA sequence in terms of probabilities of chemical words in the sequence and are computed for a set of complete genomes highly diverse in length and composition. We find the following: SI (but not divergence) is inversely proportional to sequence length for a random sequence but is length-independent for genomes; the genomic SI is always greater and, for shorter words and longer sequences, hundreds to thousands times greater than the SI in a random sequence whose length and composition match those of the genome; genomic SIs appear to have word-length dependent universal values. The universality is inferred to be an evolution footprint of a universal mode for genome growth.Comment: 4 pages, 3 tables, 2 figure

Poly[[μ4-naphthalene-1,4-dicarboxyl­ato-κ4 O:O′:O′′:O′′′-μ2-naphthalene-1,4-dicarboxyl­ato-κ4 O,O′:O′′,O′′′-bis­(2-phenyl-1H-1,3,7,8-tetra­azacyclopenta­[l]phenanthrene-κ2 N 7,N 8)dimanganese(II)] N,N-dimethyl­formamide solvate]

One of the two 1,4-dicarboxyl­ate dianions in the title compound, [Mn2(C12H6O4)2(C19H12N4)2]·C3H7NO, uses its two carboxyl­ate groups to chelate two N-heterocycle-chelated Mn atoms; the other 1,4-dicarboxyl­ate dianion binds to four such metal centers. The octa­hedrally coordinated Mn atoms are linked through the two dianions into a layer motif; the dimethyl­formamide mol­ecules occupy the spaces between adjacent layers. Ten C atoms and attached H atoms of one dianion are disordered equally over two positions