A Simple Product Formula for Certain Kazhdan-Lusztig R-Polynomials

We give a new characterization of the analytic spread of ideals in local rings with infinite residue fields. This new characterization answers a question of Huneke and can simplify Huneke's constructions in [1]     

Heegner divisors in the moduli space of genus three curves

S. Kondo used periods of surfaces to prove that the moduli space of genus three curves is birational to an arithmetic quotient of a complex 6-ball. In this paper we study Heegner divisors in the ball quotient, given by arithmetically defined hyperplane sections of the ball. We show that the corresponding loci of genus three curves are given by hyperelliptic curves, singular plane quartics and plane quartics admitting certain rational ``splitting curves'.

     

Graphic Calculators and Micro-Straightness: Analysis of a Didactic Engineering

This paper concerns the analysis of a didactic engineering, the aim of which is to introduce Calculus, at secondary-school level, through the relationship between global and local points of view. It was designed for a graphic–symbolic calculator environment and structured in accordance with a learning trajectory from identifying the graphical phenomenon of local linearity to its mathematical formulation. This learning trajectory involves the reconstruction of the relationship with the tangent line to a curve at a chosen point. The analysis shows the use of different semiotic systems in order to grasp this phenomenon and construct its mathematical meaning.

Deposition and characterization of a CoHCF nanorod array in a templated ormosil film on an electrode and application to electrocatalysis

Cobalt hexacyanoferrate (CoHCF) was electrodeposited into an organically modified silica (ormosil) film with a nanoarray of parallel, cylindrical channels, which were obtained using 20-nm poly(styrene sulfonate), PSS, beads as a templating agent. The PSS was bound to the electrode surface with 3-aminopropyltriethoxysilane, APTES. Methoxytrimethylsilane was the ormosil precursor. Electrochemically assisted processing at a positive potential where the hydrogen ion catalyst was generated was used to deposit the ormosil film. Subsequently, the PSS and APTES were removed to provide the pores. The CoHCF was deposited in the 20-nm channels by cyclic voltammetry of a freshly prepared K₃Fe(CN)₆, CoCl₂ mixture with 1.0 mol dm^?3 KCl as the supporting electrolyte. Limiting the number of electrodeposition cycles to 10–20 resulted in CoHCF nanorods in the pores, whereas with 50 cycles bulk-form CoHCF spilled over the outer ormosil surface. Electrocatalytic oxidation of cysteine was successfully performed on these nanorod arrays, which showed greater catalytic activity than bulk-form CoHCF.     

2-substituted benzofuran fragment ion formation in the electron ionization mass spectra of 6-alkyl- and 6-aryldibenzo(d,f)(1,3)dioxepine derivatives. 1. Spirocyclization of the molecular ions in the gas phase

The formation of 2-substituted benzo[b]furan ions in the electron ionization (EI) mass spectra of a series of 6-alkyl- and 6-aryldibenzo(d,f)(1,3)dioxepines has been studied by means of exact mass measurements and multiple-stage mass spectrometry conditions using an ion trap mass spectrometer. The proposed mechanism of formation of benzo[b]furan ions requires the formation of a spirocyclic cyclohexadienone system, which undergoes elimination of a cyclopentadienone molecule. A parallel with the chemical conversion of arylmethyl-substituted dibenzo(d,f)(1,3)dioxepines into an analogous spirocyclic system was also underlined.     

Two new sesquiterpene lactones from the leaves of Laurus nobilis

As a part of our ongoing interest in new bioactive compounds from natural sources, we studied Laurus nobilis (Lauraceae). This plant is widespread in the Mediterranean area and is used for medicinal and economic purposes. Chromatographic separations on active extracts led to the isolation of two new sesquiterpene lactones, 5a,9-dimethyl-3-methylene-3,3a,4,5,5a,6,7,8-octahydro-1-oxacyclopenta[c]azulen-2-one (1) and 3beta-chlorodehydrocostuslactone (2). The structures of the new compounds were identified by 1D and 2D NMR experiments, as well as high resolution mass spectrometry. The cytotoxic activity was also evaluated against three different tumor cell lines of human origin.     

Inactivation of vascular smooth muscle cells photosensitised by liposome-delivered Zn(II)-phthalocyanine

Photodynamic therapy is a promising approach for the prevention of arterial restenosis, which frequently occurs after balloon angioplasty, largely owing to abnormal proliferation of vascular smooth muscle cells (VSMC) and their migration from the media to the intima, where they originate intimal hyperplasia (IH). We investigated the efficacy of Zn(II)-phthalocyanine-photosensitised processes in promoting the inactivation of VSMC. This liposome delivered phthalocyanine is readily taken up by VSMC, largely partitions in the Golgi apparatus, and upon photoactivation causes >95% cell mortality using mild irradiation conditions (e.g. 5 min irradiation at 1 microM ZnPc). Cell death occurs through the parallel development of random necrotic and apoptotic processes.     

X-ray illumination induced Fe(II) spin crossover in the Prussian blue analogue cesium iron hexacyanochromate

The effect of X-ray illumination on the structural properties of the mixed valence Prussian blue analogue CsFe(II)[Cr(III)(CN)6] has been studied by time-dependent high-resolution synchrotron X-ray diffraction. Abrupt isosymmetric phase transitions, accompanied by dramatic volume collapse, were found in the temperature range 245-265 K, induced by sudden Fe(II) spin transitions from the high spin (HS) (4t(2g)2e(g), S = 2) to the low spin (LS) (6t(2g)0e(g), S = 0) configuration. Absorption of X-ray photons generates photoexcited Fe(II)(LS) domains whose size rapidly grows with time until the percolation threshold is reached and the structure collapse is triggered. The persistent character of the optically excited spin crossover states derives from the strong electron-phonon coupling, associated with the large lattice relaxations, which accompany the internal spin rearrangements. It is thus possible to use X-ray light in a controllable and efficient way to induce photoswitching between the ground and hidden or inaccessible excited states in suitably selected multistable materials in the bulk.     

Synthesis of indoles by intermolecular cyclization of unfunctionalized nitroarenes and alkynes, catalyzed by palladium-phenanthroline complexes

Palladium-phenanthroline complexes efficiently catalyze the reaction of nitroarenes with arylalkynes and CO to give 3-arylindoles by an ortho-C-H functionalization of the nitroarene ring. Both electron-withdrawing and electron-donating substituents are tolerated on the nitroarene, except for bromide and activated chloride. Nitroarenes bearing electron-withdrawing substituents react faster, but the selectivity of the reaction depends on both polar and radical stabilization effects. Among those tested, only arylalkynes afforded indoles under the investigated conditions. The reaction mechanism was partly investigated. The kinetics is first order in nitroarene concentration and the rate-determining step of the cycle is the initial nitroarene reduction. No primary isotope effect is observed on either rate or selectivity, implying that the cyclization step is fast.