Cell transfer and monomial positivity

We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomial-positivity is to be expected of a large class of generating functions with combinatorial definitions similar to Schur functions. These generating functions are defined on posets with labelled Hasse diagrams and include for example generating functions of Stanley's (P,ω)-partitions. T.L. was supported in part by NSF DMS-0600677.     

Mass spectrometric identification of cyclic polysulfides in sediment of the Eastern Gulf of Finland. I

Structures of six cyclic polysulfides, previously unknown as organic environmental pollutants, were analyzed from a sediment sample from the Eastern Gulf of Finland. The determinations were done by gas chromatography connected to mass spectrometry. High resolution (HRMS) measurements of the isotopic composition of four compounds could be done to confirm their molecular formulae. Total low resolution (LRMS) spectra were used to elucidate structures of all six compounds by thermochemical approach, application of fragmentation rules and by ICLU simulation of the spectra. The compounds were deduced to be (in the order of GC- retention) 1,2,4-trithiacycloheptane, tetrathiacyclopentane, 1,2,4,5-tetrathia-cyclohexane, 1,2,3,4- tetrathiacycloheptane, 1,2,3,4-tetrathiacyclohexane and 1,2,4,6-tetrathiacyclooctane.     

Three polymorphs of 3‐(3‐phenyl‐1H‐1,2,4‐triazol‐5‐yl)‐2H‐1‐benzopyran‐2‐one formed from different solvents

The polymorphic study of 3‐(3‐phenyl‐1H‐1,2,4‐triazol‐5‐yl)‐2H‐1‐benzopyran‐2‐one, C₁₇H₁₁N₃O₂, was performed due to its potential biological activity and revealed three polymorphic modifications in the triclinic space group P, the monoclinic space group P2₁ and the orthorhombic space group Pbca. These polymorphs have a one‐column layered type of crystal organization. The strongest interactions between the molecules of the studied structures is stacking between π‐systems, while N—H…N and C—H…O hydrogen bonds link stacked columns forming layers as a secondary basic structural motif. C—H…π hydrogen bonds were observed between neighbouring layers and their role is the least significant in the formation of the crystal structure. Packing differences between the polymorphic modifications are minor and can be identified only using an analysis based on a comparison of the pairwise interaction energies.     

Biological properties of two enantiomorphic forms of N‐(2,6‐dimethylphenyl)‐4‐hydroxy‐2,2‐dioxo‐1H‐2λ6,1‐benzothiazine‐3‐carboxamide,a structural analogue of piroxicam

The title benzothiazine‐3‐carboxamide, C₁₇H₁₆N₂O₄S, crystallized in two enantiomorphic crystal forms with the space groups P3₂ and P3₁ despite the absence of a classic stereogenic atom. The molecular structures are mirror images of each other. Only one sulfonyl O atom takes part in intramolecular hydrogen bonding as a proton acceptor and this atom is different in the two enantiomorphic structures. As a result, the S atom becomes a pseudo‐stereogenic centre. This fact is worth taking into account due to the different biological activities of the enantiomorphic forms. One form possesses a high analgesic activity, while the other form revealed a high anti‐inflammatory activity.