Eigenvalue Asymptotics of the Stokes Operator for Fractal Domains

The leading asymptotic term for the function that counts theeigenvalues of the Stokes operator is determined for fairlygeneral underlying bounded domains. Moreover, the remainderis estimated in terms of the fractality of the boundary of thedomain. The results obtained resemble corresponding ones forthe Dirichlet Laplacian. 1991 Mathematics Subject Classification:35P20.     

Short range order and glass transition in AgIAg2OB2O3 vitreous electrolytes

Several experimental techniques are used to study the short range order, the dynamics and the glass transition in AgIAg₂B₂O₃ compounds. Addition of Ag₂O to B₂O₃, up to [Ag₂O]/[B₂O₃] ?0.5 modifies the borate network by creating a BO₄ unit for each silver added. Addition of AgI decreases the glass transition temperature (T_g) but has only minor effects on the short range structure of the borate network. Silver iodide is partially accomodated in the interstices of the glass network. The relationship among a tentative structural picture, the ion transport phenomena and the low temperature dynamics are discussed.An investigation of the dynamics in the AgI·Ag₂O·2B₂O₃ glass near and above T_g is presented. With NMR techniques, we monitor the onset of tumbling of the borate units and the dynamical effects of crystallization and/or aging of the glass. Hysteresis effects in the ionic conductivity (σ) temperature dependence and the non-Arrhenian behavior of σT near T_g are interpreted in terms of structural modifications occurring at elevated temperatures in the glass.     

A lower bound for the equilateral number of normed spaces

We show that if the Banach-Mazur distance between an -dimensional normed space and is at most , then there exist equidistant points in . By a well-known result of Alon and Milman, this implies that an arbitrary -dimensional normed space admits at least equidistant points, where is an absolute constant. We also show that there exist equidistant points in spaces sufficiently close to , .

     

Assessment of water-soluble pi-extended squaraines as one- and two-photon singlet oxygen photosensitizers: design, synthesis, and characterization

Singlet oxygen sensitization by organic molecules is a topic of major interest in the development of both efficient photodynamic therapy (PDT) and aerobic oxidations under complete green chemistry conditions. We report on the design, synthesis, biology, and complete spectroscopic characterization (vis-NIR linear and two-photon absorption spectroscopy, singlet oxygen generation efficiencies for both one- and two-photon excitation, electrochemistry, intrinsic dark toxicity, cellular uptake, and subcellular localization) of three classes of innovative singlet oxygen sensitizers pertaining to the family of symmetric squaraine derivatives originating from pi-excessive heterocycles. The main advantage of pi-extended squaraine photosensitizers over the large number of other known photosensitizers is their exceedingly strong two-photon absorption enabling, together with sizable singlet oxygen sensitization capabilities, for their use at the clinical application relevant wavelength of 806 nm. We finally show encouraging results about the dark toxicity and cellular uptake capabilities of water-soluble squaraine photosensitizers, opening the way for clinical small animal PDT trials.     

DEA with non-monotonic variables. Application to EU governments’ macroeconomic efficiency

Conventional Data Envelopment Analysis (DEA) considers monotonic variables, ie the lower the inputs and the larger the outputs, the better. There are, however, occasions when the monotonicity of a variable with respect to efficiency depends on the value of the variable, that is in a certain range of values an increase in the variable is desirable, while in another range it is a decrease of the variable that is desirable. In this paper, a DEA model that solves problems considering non-monotonic variables is proposed. An application to assess the macroeconomic efficiency of European Union Member States, as regards taxation, gross debt, GDP growth and employment is presented.     

Colour quenching corrections on the measurement of 90Sr through Cerenkov counting

The determination of ⁹⁰Sr through the Cerenkov radiation emitted by its descendant ⁹⁰Y is a well-known method and firmly established in literature. Nevertheless, in order to obtain an accurate result based on a Cerenkov measurement, the experimental work must be extremely rigorous because the efficiency of Cerenkov counting is especially sensitive to the presence of colour. Any traces of colour in the sample produce a decrease in the number of photons detected in the photomultipliers and, therefore, this might cause a diminution in Cerenkov counting efficiency. It is essential not only to detect the effect of colour quenching in the sample but also to correct the decrease in counting efficiency. For this reason, colour quenching correction curves versus counting efficiency are usually done when measuring through Cerenkov counting. One of the most widely used techniques to evaluate colour quenching in these measurements is the channel ratio method, which consists of the measurement of the shift of the spectrum measuring the ratio of counts in two different windows. The selection of the windows for the application of the corrections might have an influence on the quality of the fitting parameters of the correction curves efficiency versus colour quenching degree and hence on the final ⁹⁰Sr result. This work is focused on the calculation of the counting efficiency decrease using the channel ratio method and on obtaining the best fitting correction curve. For this purpose, empirical curves obtained through artificial quenchers have been studied and the results have been tested in real samples. Additionally, given that the Packard Tri-Carb 3170 TR/SL liquid scintillation counter is a novel detector for use in Cerenkov counting, the previous calibration of the Tri-Carb 3170 TR/SL detector, necessary for the measurement of ⁹⁰Sr, is included.     

Damage morphology of Kr ion tracks in apatite: dependence on dE/dX

With the aim of characterizing damage along nuclear tracks in apatite, Durango fluoroapatite monocrystals were irradiated under a high fluence ⁸⁶Kr ion beam at the G.A.N.I.L. (Grand Accélérateur National d'Ions Lourds, Caen, France). The resulting irradiation damage was studied by associating CRBS spectrometry and chemical etching. By applying Poisson's law to the backscattering results, the nuclear track average effective radius R_e was calculated for different steps along the ion path. On the other hand, the chemical etching experiments allowed us to deduce three different damaging morphologies in correspondence to the R_e values. For the first time in apatite, it has been shown that a defect fragmentation produced along the ion paths may be detected by chemical etching. These results were also applied to fission tracks in order to quantify the damage rate and to describe the damage morphology evolution along fission fragment paths.     

Analysis of phytochelatin-cadmium complexes from plant tissue culture using nano-electrospray ionization tandem mass spectrometry and capillary liquid chromatography/electrospray ionization tandem mass spectrometry.

Phytochelatins (PCs, also known as class III metallothioneins), a family of sulfhydryl-rich peptides with the formula (gamma-GluCys)(n)Gly(Pc(n), n = 2-11), are induced in plants, yeast and fungi exposed to heavy metals, and are thought to detoxify metals by forming PC- metal complexes. Although PCs have been detected, PC- metal complexes have not been well characterized. In this work, nano-electrospray ionization tandem mass spectrometry (nano-ESI-MS/MS) and capillary liquid chromatography/electrospray ionization tandem mass spectrometry (capillary LC/ESI-MS/MS) methods were used to analyze PC - Cd complexes isolated from Datura innoxia, also known as Jimsonweed, cell culture exposed to Cd. With nano-ESI-MS/MS and capillary LC/ESI-MS/MS we could simultaneously detect the presence of PCs and PC - Cd complexes from plant cell extracts, unambiguously identify these species and elucidate the nature of individual PC - Cd complexes. Phytochelatins with n = 3-6 were detected, as were PC - Cd complexes with PC(3), PC(4) and PC(5). This is the first study to report the size and nature of native PC - Cd complexes from plant tissue samples. These results demonstrate that the direct analysis of plant extracts using nano-ESI-MS/MS and capillary LC/ESI-MS/MS methods is simple and sensitive to the range of PCs and PC - Cd complexes in plants. Hence these methods open up new opportunities for further quantitative analysis of PCs and PC - metal complexes in cell culture and plant systems to understand the relationship between the biosynthesis of these compounds and metal tolerance.