Curvature Tensors Whose Jacobi or Szabo Operator is Nilpotent on Null Vectors

The authors show that any k-Osserman Lorentzian algebraic curvaturetensor has constant sectional curvature, and give an elementaryproof that any local 2-point homogeneous Lorentzian manifoldhas constant sectional curvature. They also show that a SzabóLorentzian covariant derivative algebraic curvature tensor vanishes.2000 Mathematics Subject Classification 53B20.     

Polarization reflection holographic gratings in azobenzene-containing gelatine films

We have written polarization reflection holograms in an azobenzene-containing material. Two waves with circular polarization were used to record the gratings; the light resulting from their overlap induces chirality in the samples. The holographic reflection of the polarization gratings has the properties of Bragg reflection in cholesteric liquid crystals.     

Anomalous diffusion in living yeast cells

The viscoelastic properties of the cytoplasm of living yeast cells were investigated by studying the motion of lipid granules naturally occurring in the cytoplasm. A large frequency range of observation was obtained by a combination of video-based and laser-based tracking methods. At time scales from 10(-4) to 10(2) s, the granules typically perform subdiffusive motion with characteristics different from previous measurements in living cells. This subdiffusive behavior is thought to be due to the presence of polymer networks and membranous structures in the cytoplasm. Consistent with this hypothesis, we observe that the motion becomes less subdiffusive upon actin disruption.     

Prediction of the surface tension of surfactant mixtures for detergent formulation using Design Expert software

Abstract  

The formulation of a detergent product is a complicated task which depends on many economical, ecological, and practical parameters. The goal is to achieve a product which will have optimal washing properties and significantly decrease the surface tension. Therefore, prediction of the minimal surface tension of a mixture of four different surfactants can be very beneficial for the industry. In this work this task was performed by using Stat-Ease Design Expert software. This program was successfully applied for prediction of the minimal surface tension and optimization of the composition of different surfactant mixtures. Predicted data were compared with experimental results, and very good correlation was achieved. For further application, more complex optimization procedures could be performed by adding additional parameters to the Design Expert software. Therefore, this program is extremely useful for the laundry industry and could be successfully applied in many other, more complex tasks.     

Schur‐convexity and quadrature formulae

This paper aims to contribute to the exploration of quadrature formulae by proving that the error of a quadrature formula has the Schur‐convexity property. The emphasis is on the quadrature formulae with the maximum degree of precision. The Schur‐convexity of the error has an interesting implication – the monotonicity of the error. Namely, it turns out that the absolute value of the error is always smaller on a smaller interval (of the two which share the same midpoint).     

Circular Dichroism of Some 2-(Phenylmethyl)pyridine Derivatives

The absolute configuration of the 2-(phenylmethyl)pyridine derivatives 1 – 9 had been established by X-ray diffraction and chemical correlation. Their CD spectra have been studied in different solvents for the free and protonated forms. It has now been found that, from the sign of the strong CD couplet between 270 and 220 nm, which was observable for all these compounds besides 7 and 9 , their absolute configuration can be determined much quicker.     

A Particulate Biochromatographic Support for the Research of Arginase Inhibitors Doped with Nanomaterials: Differences Observed Between Carbon and Boron Nitride Nanotubes. Application to Three Plant Extracts

The arginase enzyme was bound to porous silica using a reactive polymer where two types of nanomaterials were entrapped, i.e., carbon nanotubes (CNTs) and boron nitride nanotubes (BNNTs). For the first time, it was shown that BNNTs were highly efficient for increasing the performance of a particulate bioactive support. Also, we demonstrated that BNNTs enhanced more strongly this effect in comparison with CNTs. In addition, with this novel bioactive support, the relative IC50 values of the well-known arginase inhibitors were found to be in agreement with those derived by the conventional spectrometric method. It was shown the ethylacetate extract of the roots of Spirotropis longifolia (SL) and of the ethanol extract of sunflower (Helianthus annuus) seed (SS) and Lonicera japonica Thunb, i.e., honeysuckle (H) on the arginase activity inhibited the enzyme activity.     

Comparison of sample preparation methods for the ICP-AES determination of minor and major elements in clarified apple juices

Inductively coupled plasma atomic emission spectrometry (ICP-AES) was used for the determination of minor and major elements present in apple juices. Prior to ICP-AES measurement, samples were diluted with nitric acid or digested in a microwave assisted digestion system. The differences in the measured element concentrations after application of different types of sample preparation procedures are discussed. The direct measurement compared to closed microwave dissolution was found to be the best sample preparation procedure. Prior to the measurements the ICP-AES method was validated and optimized for the determination of elements in apple juices. For diluted apple juice samples the lowest limits of detection (LOD) were obtained for Ba and Cd (< 20 μg L^{− 1}), moderate ones for Cu, Mn, Ni, Fe, Ag, Ca, Cr, Zn, Mg, and Sr (20–100 μg L^{− 1}), and the highest LODs for K, Pb, Na, and Al (> 110 μg L^{− 1}). The results obtained for the repeatability (< 0.9%), the intermediate precision (< 4.5%), the day-to-day reproducibility (< 5.2%), and the overall uncertainty of measurement (approx. 4–7%) for all elements analyzed demonstrated the good applicability of the proposed method. Differences in major element content in fresh and commercial apple juice are discussed.