The limiting behavior on the restriction of divisor classes to hypersurfaces

Let A be an excellent local normal domain and {f_n}_n=1^∞ a sequence of elements lying in successively higher powers of the maximal ideal, such that each hypersurface A/f_nA satisfies R₁. We investigate the injectivity of the maps Cl(A)→Cl((A/f_nA)′), where (A/f_nA)′ represents the integral closure. The first result shows that no non-trivial divisor class can lie in every kernel. Secondly, when A is, in addition, an isolated singularity containing a field of characteristic zero, dim A?4, and A has a small Cohen-Macaulay module, then we show that there is an integer N>0 such that if , then Cl(A)→Cl((A/f_nA)′) is injective. We substantiate these results with a general construction that provides a large collection of examples.     

Molecular origin and dynamic behavior of slip in sheared polymer films

The behavior of the slip length in thin polymer films subject to planar shear is investigated using molecular dynamics simulations. At low shear rates, the slip length extracted from the velocity profiles correlates well with that computed from a Green-Kubo analysis. Beyond chain lengths of about N=10, the molecular weight dependence of the slip length is dominated strongly by the bulk viscosity. The dynamical response of the slip length with increasing shear rate is well captured by a power law up to a critical value where the momentum transfer between wall and fluid reaches its maximum.     

Unexpected single-step formation of 1,2-anti-heterodisubstituted calix[4]arenes upon alkylation of a tribenzoyl precursor

The selective preparation and complete structural characterization of a small series of 1,2-anti-heterodisubstituted calix[4]arenes has been accomplished. These compounds were obtained in two steps from unsubstituted p-tert-butylcalix[4]arene by tribenzoylation and a subsequent one-pot, two-step sequence involving alkylation with simultaneous partial deacylation, resulting in heterodisubstituted calixarenes carrying an alkyl and an aroyl group. The monoalkyl-tribenzoyl intermediate, prior to in situ deprotection, could also be isolated.     

Monitoring and fast detection of mycotoxin-producing fungi based on headspace solid-phase microextraction and headspace sorptive extraction of the volatile metabolites

Solid phase microextraction in combination with capillary GC-MS was used as monitoring technique for the collection and detection of the fungal volatile metabolite (+)-aristolochene by sporulated surface cultures of Penicillium roqueforti. A comparison was made between different toxigenic and nontoxigenic strains of P. roqueforti. Different growth conditions and media, such as malt extract agar, potato dextrose agar and sabouraud dextrose agar were compared. Whereas toxigenic strains produced large amounts of (+)-aristolochene, beta-elemene, valencene and germacrene A, nontoxigenic P. roqueforti strains showed a remarkably different headspace profile, in which ethyl-2-hexenoate, E-beta-caryophyllene, aromadendrene and beta-patchoulene were the predominant volatiles, apart from other sesquiterpene hydrocarbons present at lower concentrations. Stir bar sorptive extraction, was also applied in the headspace sampling mode, i.e. headspace sorptive extraction (HSSE) for the enrichment of fungal volatiles from sporulated surface cultures to differentiate between toxigenic and nontoxigenic fungi. Hence, it can be concluded that headspace analysis of volatile fungal metabolites by SPME and HSSE in combination with capillary GC-MS is a suitable monitoring technique for the fast detection of mycotoxin producing fungi.     

Cover Picture

The cover picture shows the metalloporphyrin heterodimer [(tpp)Mo$\rm{\mathop{-}^{4}}$Re(oep)](+) with the novel [Mo$\rm{\mathop{-}^{4}}$Re](5+) core. The core represents the first example of a quadruple bond between elements of different triads, thus proving that heterometallic quadruple bonds are not limited to the Group 6 metals. From the space-filling model it is clear that there is no interaction between the stabilizing porphyrin ligands. The ORTEP plot in a projection along the Re-Mo axis emphasizes the perfectly eclipsed geometry of the porphyrins, which is unambiguous proof of the existence of the quadruple bond in the solid state. The diamagnetism and large magnetic anisotropy of the cation, as determined by (1)H NMR spectroscopy, indicate that the quadruple bond is retained in solution. A logical and well-defined synthetic route was used to synthesize the dimer, and can be extended to other metalloporphyrins to generate further novel quadruple bonds (the picture was generated by Marina Boulan, St. Petersburg, Russia), full details are reported by J. P. Collman et al. on p. 1271 ff.     

Maximal monotonicity, conjugation and the duality product

Recently, the authors studied the connection between each maximal monotone operator and a family of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities.

The aim of this paper is to establish the converse of the latter fact. Namely, that every convex function satisfying those two particular inequalities is associated to a unique maximal monotone operator.

     

Nonlinear Liouville theorems for Grushin and Tricomi operators

The aim of this paper is to study necessary conditions for existence of weak solutions of the inequality