Deformation of Gabor systems

We introduce a new notion for the deformation of Gabor systems. Such deformations are in general nonlinear and, in particular, include the standard jitter error and linear deformations of phase space. With this new notion we prove a strong deformation result for Gabor frames and Gabor Riesz sequences that covers the known perturbation and deformation results. Our proof of the deformation theorem requires a new characterization of Gabor frames and Gabor Riesz sequences. It is in the style of Beurling's characterization of sets of sampling for bandlimited functions and extends significantly the known characterization of Gabor frames “without inequalities” from lattices to non-uniform sets.     

NO Fluorescence Quantification by Chitosan CdSe Quantum Dots Nanocomposites

The quantification of nitric oxide (NO) based on the quenching of the fluorescence of a nanocomposites sensor constituted by cadmium/selenium quantum dots (CdSe) stabilized by chitosan (CS) and mercaptosuccinic acid (MSA) is assessed. The optimization of the response of the CS-CdSe-MSA nanocomposites to NO was done by multivariate response surface experimental design methodologies. The highest fluorescence quenching was obtained at pH 5.5 and at room temperature. The NO quantification capability of CS-CdSe-MSA was evaluated using standard solutions and a NO donor reagent. A large linear working range from 5 to 200 μM and a limit of detection of 1.86 μM were obtained. Better quantification results were obtained using the NO donor reagent. Besides NO, the response of the fluorescence of CS-CdSe-MSA to the main reactive oxygen and nitrogen species and similar NO compounds was also assessed.     

On the Upper Limits of Oxidation States in Chemistry

The concept of oxidation state ( OS ) is based on the concept of Lewis electron pairs, in which the bonding electrons are assigned to the more electronegative element. This approach is useful for keeping track of the electrons, predicting chemical trends, and guiding syntheses. Experimental and quantum‐chemical results reveal a limit near +8 for the highest OS in stable neutral chemical substances under ambient conditions. OS =+9 was observed for the isolated [IrO₄]⁺ cation in vacuum. The prediction of OS =+10 for isolated [PtO₄]²⁺ cations is confirmed computationally for low temperatures only, but hasn't yet been experimentally verified. For high OS species, oxidation of the ligands, for example, of O^?2 with formation of ^.O^?1 and O?O bonds, and partial reduction of the metal center may be favorable, possibly leading to non‐Lewis type structures.     

Application of a polarity parameter model to the separation of fat-soluble vitamins by reversed-phase HPLC

The retention behavior of a series of fat-soluble vitamins has been established on the basis of a polarity retention model: log k = (log k)(0) + p (P(m) (N) - P(s) (N)), with p being the polarity of the solute, P(m) (N) the mobile phase polarity, and (log k)(0) and P(m) (N) two parameters for the characterization of the stationary phase. To estimate the p-values of solutes, two approaches have been considered. The first one is based on the application of a QSPR model, derived from the molecular structure of solutes and their log P(o/w), while in the second one, the p-values are obtained from several experimental measurements. The quality of prediction of both approaches has also been evaluated, with the second one giving more accurate results for the most lipophilic vitamins. This model allows establishing the best conditions to separate and determine simultaneously some fat-soluble vitamins in dairy foods.     

An optimized luciferase bioluminescent assay for coenzyme A

A new bioluminescent method for coenzyme A (CoA) quantification is described. It is based on the enzymatic conversion of dehydroluciferyl-adenylate (L-AMP) into dehydroluciferyl-coenzyme A (L-CoA) by firefly luciferase (E.C. 1.13.12.7) (LUC), which causes a flash of light that can be measured in a luminometer. The method was subjected to optimization using experimental design methodologies to obtain optimum values for the concentrations of L-AMP ([L-AMP]), luciferase ([LUC]), ATP ([ATP]) and luciferin ([LH₂]). This method has a linear response over the range of 0.25–4 μM of CoA, with a limit of detection (LOD) of 0.24 μM and a limit of quantification (LOQ) of 0.80 μM. The assay has a relative standard deviation of about 7%. By coupling this optimized procedure to bioluminescent detection, a sensible and robust method can be obtained for the analysis of CoA.     

Integral stable manifolds in Banach spaces

We establish the existence of smooth integral stable manifoldsfor sufficiently small perturbations of nonuniform exponentialdichotomies in Banach spaces. We also consider the case of anonautonomous dynamics given by a sequence of C¹ maps. The optimalsmoothness of the manifolds is obtained at the same time astheir existence, using a convenient lemma of Henry. Furthermore,we obtain not only the exponential decay of the dynamics alongthe stable manifolds, but also of its derivative. In addition,we give a characterization of the stable manifolds in termsof the maximal exponential growth rate that is allowed, we discusshow the manifolds vary with the perturbations, and we discusstheir equivariance with respect to a sequence of linear operators.     

Discrete behavior of Seshadri constants on surfaces

Working over , we show that, apart possibly from a unique limit point, the possible values of multi-point Seshadri constants for general points on smooth projective surfaces form a discrete set. In addition to its theoretical interest, this result is of practical value, which we demonstrate by giving significantly improved explicit lower bounds for Seshadri constants on and new results about ample divisors on blow ups of at general points.     

Gas-phase oxidation of Cm+ and Cm2+ --thermodynamics of neutral and ionized CmO

Fourier transform ion cyclotron resonance mass spectrometry was employed to study the products and kinetics of gas-phase reactions of Cm (+) and Cm (2+); parallel studies were carried out with La (+/2+), Gd (+/2+) and Lu (+/2+). Reactions with oxygen-donor molecules provided estimates for the bond dissociation energies, D[M (+)-O] (M = Cm, Gd, Lu). The first ionization energy, IE[CmO], was obtained from the reactivity of CmO (+) with dienes, and the second ionization energies, IE[MO (+)] (M = Cm, La, Gd, Lu), from the rates of electron-transfer reactions from neutrals to the MO (2+) ions. The following thermodynamic quantities for curium oxide molecules were obtained: IE[CmO] = 6.4 +/- 0.2 eV; IE[CmO (+)] = 15.8 +/- 0.4 eV; D[Cm-O] = 710 +/- 45 kJ mol (-1); D[Cm (+)-O] = 670 +/- 40 kJ mol (-1); and D[Cm (2+)-O] = 342 +/- 55 kJ mol (-1). Estimates for the M (2+)-O bond energies for M = Cm, La, Gd, and Lu are all intermediate between D[N 2-O] and D[OC-O] - that is, 167 kJ mol (-1) < D[M (2+)-O] < 532 kJ mol (-1) - such that the four MO (2+) ions fulfill the thermodynamic requirement for catalytic oxygen-atom transport from N2O to CO. It was demonstrated that the kinetics are also favorable and that the CmO (2+), LaO (2+), GdO (2+), and LuO (2+) dipositive ions each catalyze the gas-phase oxidation of CO to CO2 by N2O. The CmO 2 (+) ion appeared during the reaction of Cm (+) with O 2 when the intermediate, CmO (+), was not collisionally cooled - although its formation is kinetically and/or thermodynamically unfavorable, CmO 2 (+) is a stable species.     

Factorial analysis optimization of a Diltiazem kinetic spectrophotometric quantification method

A Diltiazem kinetic spectrophotometric method was optimized by factorial analysis. The experimental method is based on a two-stage reaction of Diltiazem with hydroxylamine and a ferric salt: in the first stage there is a hydroxamic acid formation; and, in the second stage there is a red colour complex ferric hydroxamate formation. The variables under investigation were: solvent; hydroxylamine, sodium hydroxide and ammonium ferric sulphate concentrations; volume of perchloric acid; and, temperature. The responses of the reactional system were the maximum absorbance, the wavelength and the reaction time at maximum absorbance. Experimental design methodologies were used in the optimization. Fractional and full factorial designs followed by optimization Box-Behnken and central composite experimental designs were used. The observed optimum conditions were: methanol as reaction solvent; hydroxylamine concentration of 9.375%; sodium hydroxide concentration of 18.750%; ferric reagent concentration of 2.000%; minimum volume of perchloric acid to neutralize the sodium hydroxide; and, room temperature as reaction temperature. With this set of experimental conditions a reaction time of 10.5 s with maximum colour development at 512 nm wavelength was achieved.