Generalized Linear Systems on Curves and Their Weierstrass Points

Let C be a projective Gorenstein curve over an algebraically closed field of characteristic 0. A generalized linear system on C is a pair (?, ε) consisting of a torsion-free, rank-1 sheaf ? on C, and a map of vector spaces ε: V → Γ(C, ?). If the system is nondegenerate on every irreducible component of C, we associate to it a 0-cycle W, its Weierstrass cycle. Then we show that for each one-parameter family of curves C _t degenerating to C, and each family of linear systems (? _t , ε _t ) along C _t , with ? _t invertible, degenerating to (?, ε), the corresponding Weierstrass divisors degenerate to a subscheme whose associated 0-cycle is W. We show that the limit subscheme contains always an “intrinsic” subscheme, canonically associated to (?, ε), but the limit itself depends on the family ? _t .     

Occupation Time of Exclusion Processes with Conductances

We obtain the fluctuations for the occupation time of one-dimensional symmetric exclusion processes with speed change, where the transition rates (conductances) are driven by a general function \(W\) . The approach does not require sharp bounds on the spectral gap of the system nor the jump rates to be bounded from above or below. We present some examples and for one of them, we observe that the fluctuations of the current are trivial, but the fluctuations of the occupation time are given by a fractional Brownian Motion. This shows that, in general, the fluctuations of the current and of the occupation time are not of same order.     

n -Heptane and methylcyclohexane transformation over a HMCM-22 zeolite. Origin of the features typical of large-or of medium-pore zeolites

The main features of methylcyclohexane (mch) and n-heptane (n-C₇) transformation at 350°C were compared for fresh samples of HMWW, HMFI and HFAU zeolites. With both reactions, the behavior of HMWW was between those of the medium HMFI and large pore HFAU zeolites. Thus, the values of turnover frequency (TOF) and of the TOF_mch/n-C7 ratio were similar with HMWW and HMFI and much higher with HFAU. In contrast, small differences were found between product distributions over HMWW and HFAU but large differences between HMWW and HMFI. These observations can be explained by alkane transformation in the large supercages with 10-MR apertures of HMWW: the narrow apertures limit diffusion of the mch within the supercages, but not the diffusion of the products which are therefore typical of the transformation within large cages hence without any steric limitation.     

Unusual coordination environment for barium cations in ion recognition conducting poly[Ni(salen)(receptor)] films

[Ni( salen)] complexes bearing different crown ether receptors were electropolymerized to give films whose voltammetric signatures responded to Ba2+. In line with DFT calculations, X-ray absorption spectroscopy (XAS) near the Ni K-edge showed the nickel local environment in the monomers and their corresponding polymers (in the presence or absence of barium) to be identical. However, the expectation of crown size-dependent barium local environment (based on geometry and donor atom availability) was not found. XAS near the Ba K-edge showed that Ba2+ in the films coordinated to only two oxygen donors, irrespective of crown size. This surprisingly low coordination number (compared to solution species) is accompanied by a higher barium/crown ratio than the anticipated 1:1 stoichiometry. The implications of these effects for design and performance of sensors based on metal ion recognition chemistry are discussed.     

Gas-phase electrophilic addition promoted by CH(3)S(+)=CH(2) ions on aromatic systems

The gas-phase methylenation reaction between CH(3)S(+)=CH(2) and alkylbenzenes, aniline, phenol and alkyl phenyl ethers, which yields [M + CH](+) and CH(3)SH, has been studied by Fourier transform ion cyclotron resonance (FT-ICR) techniques and computational chemistry at the DFT level. The methylthiomethyl cation is less reactive than methoxymethyl and, unlike the latter, is unreactive toward benzene. The calculations suggest that reaction with toluene should proceed primarily by addition at the para and ortho positions resulting in a benzyl-type ion. Reaction with aniline-2,3,4,5,6-d(5) reveals that elimination of CH(3)SD is kinetically favored by a factor of 5 over elimination of CH(3)SH. Experiments with C(6)H(6)ND(2) and theoretical calculations suggest that methylenation at the nitrogen atom is energetically favorable and likely, but the observed results may reflect some H/D scrambling, which occurs after attack at a ring position. By comparison, reaction with phenol-2,3,4,5,6-d(5) reveals that methylenation followed by elimination of CH(3)SD is kinetically favored by a factor of 3.8 over elimination of CH(3)SH. For phenol, the theoretical calculations suggest that attack by CH(3)S(+)=CH(2) at the para or ortho position is the only low-energy pathway for methylenation. However, a low-energy pathway for hydrogen scrambling is predicted by the calculations originating from the exit complex, [CH(3)SH(...) CH(2)=C(6)H(4)=OH](+), of reaction at a ring position.     

Control of properties of nanocomposites bio-based collagen and cellulose nanocrystals

Collagen is an important biomaterial because it has many applications in the biomedical sector. However, the high hydrophilicity of collagen (COL) leads to easy swelling. Thus, controlling this property is highly desirable. In this work, cellulose nanocrystals (CNCs) dispersed in glycerol (GLI) were incorporated in the matrix collagen to tailor the hydrophilicity and mechanical properties. Study of the hydrophilicity of the bio-based nanocomposite was evaluated by contact angle measurement and thermogravimetric analysis. Mechanical analyses showed that CNCs are excellent reinforcing fillers to the collagen matrix. Synchrotron small-angle X-ray scattering was employed to investigate the nanostructures of COL/GLI/CNC nanocomposites and CNC water dispersion. CNC in concentrations up to 1 wt% presents an intermediate shape between a rod and a plane with a 9.34-nm radius of gyration (R _g). Bio-based nanocomposites present two different structural levels with two types of particles with very different R _gs. At the intermediate power-law regime, a large-scale mass fractal aggregate is observed. In the high-power-law regime, it is observed scattering from primary particles smaller than 1 nm. As the CNC concentration increases, the original particle distorts from a rod to a plate. The cytotoxicity assay indicates that the collagen and nanocomposites did not affect the cell viability of rat calvarial cells in vitro.     

Influence of structural factors on the enhanced activity of moxifloxacin: a fluorescence and EPR spectroscopic study

Partition coefficients of moxifloxacin in liposomes of dimyristoyl-L-α-phosphatidylcholine or dimyristoyl-L-α-phosphatidylglycerol and water were determined by spectrophotometry and fluorimetry. The K _p values obtained were larger than those reported for most of the other fluoroquinolones, a consequence of the structural changes observed in the molecule of moxifloxacin, which in turn change its acid/base properties. Introduction of a methoxy group at position 8 and a diazabicyclonyl ring at position 7 in the basic fluoroquinolone structure alters the charge distribution at the physiological pH of 7.4, and these changes seem to be responsible for its improved antibacterial potency and broader spectrum of activity. Location studies have also been performed using fluorescence and electron paramagnetic resonance (EPR) spectroscopies. The results show that moxifloxacin must be located near the phospholipid headgroups, similar to other fluoroquinolones, but contributions from a hydrophobic component were also detected. These results suggest that the enhanced activity of this drug may be related to a more facilitated entrance into the bacterial cell, perhaps including a mediator step involving electrostatic interaction with a hydrophobic component; this step then controls the extent or orientation of insertion and improves the electrostatic interaction.