Bruhat intervals as rooks on skew Ferrers boards

We characterise the permutations π such that the elements in the closed lower Bruhat interval [id,π] of the symmetric group correspond to non-taking rook configurations on a skew Ferrers board. It turns out that these are exactly the permutations π such that [id,π] corresponds to a flag manifold defined by inclusions, studied by Gasharov and Reiner.Our characterisation connects the Poincaré polynomials (rank-generating function) of Bruhat intervals with q-rook polynomials, and we are able to compute the Poincaré polynomial of some particularly interesting intervals in the finite Weyl groups An and Bn. The expressions involve q-Stirling numbers of the second kind, and for the group An putting q=1 yields the poly-Bernoulli numbers defined by Kaneko.     

Bounds and Numerical Results for Homogenized Degenerated p-Poisson Equations

In this paper we derive upper and lower bounds on the homogenized energy density functional corresponding to degenerated p-Poisson equations. Moreover, we give some non-trivial examples where the bounds are tight and thus can be used as good approximations of the homogenized properties. We even present some cases where the bounds coincide and also compare them with some numerical results.     

Regioselective alkylation of guanine via diacyloxyglyoxal-N2-acetylguanine adduct to obtain 7-alkylguanine derivatives. Studies on alkylation of guanine I

The acylated guanine-glyoxal adduct (I) has been alkylated with 4-bromobutyl acetate and in the presence of sodium hydride the reaction was regioselective to give 7-alkylguanine.     

Boundary Value Problems with Local Generalized Nevanlinna Functions in the Boundary Condition

For a class of abstract λ-dependent boundary value problems where a local variant of generalized Nevanlinna functions appears in the boundary condition, linearizations are constructed and their local spectral properties are investigated.     

Condensed‐Phase,Halogen‐Bonded CF3I and C2F5I Adducts for Perfluoroalkylation Reactions

A family of practical, liquid trifluoromethylation and pentafluoroethylation reagents is described. We show how halogen bonding can be used to obtain easily handled liquid reagents from gaseous CF₃I and CF₃CF₂I. The synthetic utility of the new reagents is exemplified by a novel direct arene trifluoromethylation reaction as well as adaptations of other perfluoroalkylation reactions.     

Characterization of Glycan Structures of Chondroitin Sulfate-Glycopeptides Facilitated by Sodium Ion-Pairing and Positive Mode LC-MS/MS

Purification and liquid chromatography-tandem mass spectrometry (LC-MS/MS) characterization of glycopeptides, originating from protease digests of glycoproteins, enables site-specific analysis of protein N- and O-glycosylations. We have described a protocol to enrich, hydrolyze by chondroitinase ABC, and characterize chondroitin sulfate-containing glycopeptides (CS-glycopeptides) using positive mode LC-MS/MS. The CS-glycopeptides, originating from the Bikunin proteoglycan of human urine samples, had ΔHexAGalNAcGlcAGalGalXyl-O-Ser hexasaccharide structure and were further substituted with 0-3 sulfate and 0-1 phosphate groups. However, it was not possible to exactly pinpoint sulfate attachment residues, for protonated precursors, due to extensive fragmentation of sulfate groups using high-energy collision induced dissociation (HCD). To circumvent the well-recognized sulfate instability, we now introduced Na⁺ ions to form sodiated precursors, which protected sulfate groups from decomposition and facilitated the assignment of sulfate modifications. Sulfate groups were pinpointed to both Gal residues and to the GalNAc of the hexasaccharide structure. The intensities of protonated and sodiated saccharide oxonium ions were very prominent in the HCD-MS2 spectra, which provided complementary structural analysis of sulfate substituents of CS-glycopeptides. We have demonstrated a considerable heterogeneity of the bikunin CS linkage region. The realization of these structural variants should be beneficial in studies aimed at investigating the importance of the CS linkage region with regards to the biosynthesis of CS and potential interactions to CS binding proteins. Also, the combined use of protonated and sodiated precursors for positive mode HCD fragmentation analysis will likely become useful for additional classes of sulfated glycopeptides.

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Thickness difference induced pore structure variations in cellulosic separators for lithium-ion batteries

The pore structure of the separator is crucial to the performance of a lithium-battery as it affects the cell resistance. Herein, a straightforward approach to vary the pore structure of Cladophora cellulose (CC) separators is presented. It is demonstrated that the pore size and porosity of the CC separator can be increased merely by decreasing the thickness of the CC separator by using less CC in the manufacturing of the separator. As the pore size and porosity of the CC separator are increased, the mass transport through the separator is increased which decreases the electrolyte resistance in the pores of the separator. This enhances the battery performance, particularly at higher cycling rates, as is demonstrated for LiFePO₄/Li half-cells. A specific capacity of around 100 mAh g^?1 was hence obtained at a cycling rate of 2 C with a 10 µm thick CC separator while specific capacities of 40 and close to 0 mAh g^?1 were obtained for separators with thicknesses of 20 and 40 µm, respectively. As the results also showed that a higher ionic conductivity was obtained for the 10 µm thick CC separator than for the 20 and 40 µm thick CC separators, it is clear that the different pore structure of the separators was an important factor affecting the battery performance in addition to the separator thickness. The present straightforward, yet efficient, strategy for altering the pore structure hence holds significant promise for the manufacturing of separators with improved performance, as well as for fundamental studies of the influence of the properties of the separator on the performance of lithium-ion cells.