Distribution of values of σ2 (n) in residue classes

IntegersN for which ₂ (n has weak uniform distribution (modN) are determined.     

Narrow band quantitative and multivariate electroencephalogram analysis of peri-adolescent period

ABSTRACT: BACKGROUND: The peri-adolescent period is a crucial developmental moment of transition from childhood to emergent adulthood. The present report analyses the differences in Power Spectrum (PS) of the Electroencephalogram (EEG) between late childhood (24 children between 8 and 13 years old) and young adulthood (24 young adults between 18 and 23 years old). RESULTS: The narrow band analysis of the Electroencephalogram was computed in the frequency range of 0--20 Hz. The analysis of mean and variance suggested that six frequency ranges presented a different rate of maturation at these ages, namely: low delta, delta-theta, low alpha, high alpha, low beta and high beta. For most of these bands the maturation seems to occur later in anterior sites than posterior sites. Correlational analysis showed a lower pattern of correlation between different frequencies in children than in young adults, suggesting a certain asynchrony in the maturation of different rhythms. The topographical analysis revealed similar topographies of the different rhythms in children and young adults. Principal Component Analysis (PCA) demonstrated the same internal structure for the Electroencephalogram of both age groups. Principal Component Analysis allowed to separate four subcomponents in the alpha range. All these subcomponents peaked at a lower frequency in children than in young adults. CONCLUSIONS: The present approaches complement and solve some of the incertitudes when the classical brain broad rhythm analysis is applied. Children have a higher absolute power than young adults for frequency ranges between 0-20 Hz, the correlation of Power Spectrum (PS) with age and the variance age comparison showed that there are six ranges of frequencies that can distinguish the level of EEG maturation in children and adults. The establishment of maturational order of different frequencies and its possible maturational interdependence would require a complete series including all the different ages.     

New Enantioselective Routes to Cyclic and Acyclic S,O-acetals; Enzymatic Resolution of α-Acetoxy Sulfides and Enantioselective Synthesis of the Antiviral Agent Lamivudine

A new method for the synthesis of cyclic and acyclic optically active S,O-acetals is reported, along with subsequent stereocontrolled transformations, culminating in a synthesis of the important antiviral nucleoside Lamivudine.     

Femtosecond laser erasing and rewriting of self-organized planar nanocracks in fused silica glass

Tightly focused, linearly polarized, femtosecond laser radiation can produce highly birefringent nanograting structures inside fused silica glass. Here we report that when the polarization direction of the femtosecond light is changed, old nanogratings are erased and simultaneously replaced with new ones whose orientation is solely determined by the polarization of the rewrite beam. We also show that these volume nanogratings can be rewritten 1000 times with little degradation in their quality.     

Simulation of a Helicon plasma source using a multivariable fuzzymodel

This paper reports work on the development of an automatic control system for a Helicon plasma processing source. The lack of a definitive physical model for the plasma physics of the source and the power coupling mechanism to the plasma precludes the use of traditional control algorithms. This paper develops a fuzzy model that simulates the behavior of the plasma source using the process of genetic algorithms to identify and optimize the parameters of the fuzzy model. This type of model will eventually be used to test a fuzzy control system for the plasma source. In this work, an extensive set of experimental data was acquired where the magnetic field and input power to the plasma source were varied over a wide range while the electron number density was measured. From this learning dataset, the genetic algorithm derived the values of the parameters for the difference equation that describes the system. The fuzzy model so constructed was used to predict the behavior of the source from known input parameters. Comparing the predictions with experimental observations showed that the fuzzy model was generally able to predict the behavior of the plasma as its input parameters were varied with a precision of better than 10%     

Gold cluster carbonyls: vibrational spectroscopy of the anions and the effects of cluster size, charge, and coverage on the CO stretching frequency

We report the vibrational spectra of the carbonyl complexes of anionic gold clusters in the range of the CO stretching frequency as measured in the gas phase using IR multiple photon dissociation spectroscopy. The investigated complexes contain between 3 and 14 Au atoms and up to 7 CO ligands. Special attention is given to the complexes that exhibit saturation CO coverage as well as to the monocarbonyl species. In conjunction with data from the corresponding cationic complexes we quantify how the CO stretching frequency varies with the charge state of the gold cluster. Our results provide a size- and charge-dependent basis to interpret values of the CO stretching frequency measured for CO on deposited gold clusters in terms of the charge states of the clusters.     

Simple method for the assay of linezolid in Brain Heart Infusion broth by high-performance liquid chromatography

A simple HPLC method was developed and validated for quantification of linezolid in Brain Heart Infusion (BHI) broth. Eperezolid was employed as internal standard and the sample pre-treatment procedure was simple. Calibration standards ranged from 0.05 to 16 mg/L. Accuracy was within 7.8% and reproducibility (RSD) was less than 8.3%. Recovery was approximately 100% at all concentrations examined. Linezolid was stable in the autosampler insert for at least 24 h at ambient temperature and in BHI for 72 h at 37 degrees C. This assay is rapid and ideal for analysis of a large number of samples.     

Studies on the Lewis acid mediated cleavage of alpha-aminoacetals: synthesis of novel 1,2-aminoethers,and evidence for alpha-alkoxy aziridinium ion intermediates

The nucleophilic cleavage of alpha-amino acetals induced by TMSOTf can be used to prepare a wide range of substituted 1,2-aminoethers. In particular, organometallic reagents, N-heterocycles, and enamines all react efficiently to give products in good yield. In appropriate cases, good levels of stereocontrol are possible, but this is very dependent on the nature of the nucleophile and the substrate, with diethylzinc proving particularly effective across a range of substrates. The degree of stereocontrol can be used to infer the nature of the reactive intermediates involved in the reaction. With diethylzinc, it is most likely that the reaction proceeds by coordination of the nucleophile to the amino group followed by transfer of an ethyl group to an alpha-oxocarbenium ion. With non-coordinating nucleophiles, the stereochemical outcome can be rationalised in terms of addition to the possible alpha-alkoxy aziridinium ion intermediates.