On the rate of points in projective spaces

The rate of a standard gradedK-algebraR is a measure of the growth of the shifts in a minimal free resolution ofK as anR-module. It is known that rate(R)=1 if and only ifR is Koszul and that rate(R) ≥m(I)−1 wherem(I) denotes the highest degree of a generator of the defining idealI ofR. We show that the rate of the coordinate ring of certain sets of pointsX of the projective space P ⁿ is equal tom(I)−1. This extends a theorem of Kempf. We study also the rate of algebras defined by a space of forms of some fixed degreed and of small codimension.     

EEG Fractal Analysis Reflects Brain Impairment after Stroke

Stroke is the commonest cause of disability. Novel treatments require an improved understanding of the underlying mechanisms of recovery. Fractal approaches have demonstrated that a single metric can describe the complexity of seemingly random fluctuations of physiological signals. We hypothesize that fractal algorithms applied to electroencephalographic (EEG) signals may track brain impairment after stroke. Sixteen stroke survivors were studied in the hyperacute (<48 h) and in the acute phase (∼1 week after stroke), and 35 stroke survivors during the early subacute phase (from 8 days to 32 days and after ∼2 months after stroke): We compared resting-state EEG fractal changes using fractal measures (i.e., Higuchi Index, Tortuosity) with 11 healthy controls. Both Higuchi index and Tortuosity values were significantly lower after a stroke throughout the acute and early subacute stage compared to healthy subjects, reflecting a brain activity which is significantly less complex. These indices may be promising metrics to track behavioral changes in the very early stage after stroke. Our findings might contribute to the neurorehabilitation quest in identifying reliable biomarkers for a better tailoring of rehabilitation pathways.     

Experimental and mechanistic investigation of an iodomalonic acid-based Briggs-Rauscher oscillator and its perturbations by resorcinol

Classic Briggs-Rauscher oscillators use malonic acid (MA) as a substrate. The first organic product is iodomalonic acid. Iodomalonic acid (IMA) can serve as a substrate also; thus, the first product in that case is diiodomalonic acid (I(2)MA). Nonoscillating iodination kinetics can be followed by absorbance at 462 nm in acidic KIO(3) so long as IMA is in substantial excess over [I(2)]. At 25 °C, simulations lead to the two most important rate laws, and related rate constant estimates are reported. I(2)MA eventually decomposes by unknown processes, but I(2), O(2), H(2)O(2), and Mn(2+) speed up that decomposition, liberating most of the iodine back to the solution. Resorcinol is an effective inhibitor of oscillations both in MA oscillators and in IMA oscillators. Response of an IMA oscillator to varying amounts of resorcinol is shown herein and is similar to that for MA-based oscillators. The inhibitory effect of resorcinol is diminished by addition of IMA to a MA-based oscillator. The iodination reaction between IMA and resorcinol is too slow (0.043 M(-1) s(-1)) to account for the decreased inhibitory effectiveness of resorcinol. Rather, the decomposition of I(2)MA is responsible for the inhibition decrease.     

Synthesis of polymers containing regularly distributed tetrathia‐[7]‐elicene units along the backbone

A tetrathia‐[7]‐helicene bearing in the 2 and 13 positions cyanovinyl groups was used as comonomer in the Michael‐type polyaddition reaction with N,N′‐bis(β‐mercaptoethyl)piperazine. This led to a new polymer bearing tetrathia‐[7]‐helicene units regularly distributed along the polymer backbone, which may be regarded as the first example of a new family of potentially useful nonlinear optical materials. All products were structurally characterized by ¹H and ¹³C NMR spectroscopy. Differential scanning calorimetry characterizations revealed the presence, in both monomeric and polymeric helicenes, of glass‐transition like temperatures, associated to some conformational variation of the helicene units. The optical properties, the film formation and the morphology of the polymer‐containing tetratia‐[7]‐helicenes were also investigated. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

A novel conformationally restricted analogue of 3-methylaspartic acid via stereoselective methylation of chiral pyrrolidin-2-ones

Conformationally restricted analogues of β-methylaspartic acid were easily prepared starting from chiral N-protected trans-3-amino-4-methoxycarbonyl pyrrolidin-2-ones. The key step of the synthesis was the methylation reaction at C-4, proceeding with high diastereoselection syn to the protected amino group lying at C-3 of the pyrrolidin-2-one ring.     

Length-scale-dependent relaxation in colloidal gels

We use molecular dynamics computer simulations to investigate the relaxation dynamics of a simple model for a colloidal gel at a low volume fraction. We find that due to the presence of the open spanning network this dynamics shows at low temperature a nontrivial dependence on the wave vector which is very different from the one observed in dense glass-forming liquids. At high wave vectors the relaxation is due to the fast cooperative motion of the branches of the gel network, whereas at low wave vectors the overall rearrangements of the heterogeneous structure produce the relaxation process.     

Direct determination of total mercury in phosphate rock using alkaline fusion digestion

The aim of this work was to develop a new method to determine the mercury (Hg) concentrations in phosphate rock using a dedicated analytical instrument (the DMA80 Tricell by Milestone) that employs an integrated sequence of thermal decomposition followed by catalyst conversion, amalgamation and atomic absorption spectrophotometry. However, this instrument underestimates Hg concentrations when phosphorite and apatite rocks are investigated with a classic thermal decomposition treatment that complies with US EPA method 7473.     

Determination of hydrazine in drinking water: Development and multivariate optimization of a rapid and simple solid phase microextraction-gas chromatography-triple quadrupole mass spectrometry protocol

In this work, the capabilities of solid phase microextraction were exploited in a fully optimized SPME-GC-QqQ-MS analytical approach for hydrazine assay. A rapid and easy method was obtained by a simple derivatization reaction with propyl chloroformate and pyridine carried out directly in water samples, followed by automated SPME analysis in the same vial without further sample handling. The affinity of the different derivatized compounds obtained towards five commercially available SPME coatings was evaluated, in order to achieve the best extraction efficiency. GC analyses were carried out using a GC-QqQ-MS instrument in selected reaction monitoring (SRM) acquisition mode which has allowed the achievement of high specificity by selecting appropriate precursor–product ion couples improving the capability in analyte identification. The multivariate approach of experimental design was crucial in order to optimize derivatization reaction, SPME process and tandem mass spectrometry parameters. Accuracy of the proposed protocol, tested at 60, 200 and 800 ng L⁻¹, provided satisfactory values (114.2%, 83.6% and 98.6%, respectively), whereas precision (RSD%) at the same concentration levels were of 10.9%, 7.9% and 7.7% respectively. Limit of detection and quantification of 4.4 and 8.3 ng L⁻¹ were obtained. The reliable application of the proposed protocol to real drinking water samples confirmed its capability to be used as analytical tool for routine analyses.     

Influence of synthesis conditions on the cross-link architecture of silsesquioxanes prepared by in situ water production route

The esterification reaction between carboxylic acids and alcohols has been used as the source of water for the hydrolysis-condensation reactions of difunctional and trifunctional organosilanes. Diphenylsilanediol (DPDO) has been reacted with methacryloxypropyltrimethoxysilane (MPTMS) and glycidoxypropyltrimethoxysilane (GPTMS) and the obtained products have been characterized by vibrational spectroscopy (FT-IR, FT-Raman) nuclear magnetic resonance (NMR) and gel permeation chromatography. The relation between water availability from the in situ water production process (ISWP) and silsesquioxanes morphology has been evaluated in the case of DPDO/MPTMS mixtures, changing molecular features of acids and alcohols. These measurements have shown that the pK of the carboxylic acid used in the esterification reaction has a valuable influence on the silanes cross-linking ability. Acids with low pK values and heteroatoms substituents favor the silane hydrolysis and allow the growth of high molecular weight species. Using acetic acid/ethanol mixture leads to the best results for DPDO/MPTMS reaction, with a narrow distribution of silsesquioxane species. Under the same conditions, the reaction of DPDO with GPTMS produces polymeric species and only avoiding the presence of the difunctional precursor allows to limiting the silsesquioxanes species growth.