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.     

Studies on orally active cephalosporin esters. IV. Effect of the C-3 substituent of cephalosporin on the gastrointestinal absorption in mice

The effect of the C-3 substituent on the oral absorbability of pivaloyloxymethyl (POM) ester of cephalosporin in mice is described. The C-3 substituent affects the physicochemical and biochemical properties of POM ester, such as lipophilicity, water solubility, chemical stability and enzymatic stability. Quantitative analyses of the relationships between these properties and the oral bioavailability have been attempted. Lipophilicity made a parabolic contribution to the absorption. The optimum log P octanol/water value was estimated to be around 2.22. The chemical isomerization of the cephem double bond from delta 3 to delta 2 in the intestinal lumen prior to absorption contributed linearly to decrease of absorption. In the case of POM ester having a larger isomerization rate, more delta 2 isomer was detected in feces and urine. Enzymatic hydrolysis of POM ester to the parent acid in intestinal tissue was faster for a more lipophilic ester. Hydrolytic activity, which was detected in the content of the intestinal lumen, would lower the absorption. The effect of the C-3 substituent on water solubility was not important for the absorption of cephalosporin employed in the present study. Isomerization of the double bond, which was found to be characteristic for cephalosporin ester, presented a problem in the prodrug approach for oral use.     

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.