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.     

Carbonaceous phases by IR laser-induced decomposition of 3-butyn-2-one

2 laser radiation in the gas phase results in the deposition of carbonaceous films composed of a graphitic and monohydrogenated carbon, in which H is dominantly bonded to sp³ sites. The films incorporate oxygen in the topmost layers. The technique is suitable for the preparation of thin C-based films at low substrate temperatures. Received: 23 July 1997/Accepted: 18 November 1997     

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.     

Macroporous antimony film electrodes for stripping analysis of trace heavy metals

We report on the elaboration of macroporous antimony film electrodes. The strategy to create macroporous electrodes is based on the replication of colloidal crystal templates. These electrodes of controlled porosity show an increased internal electroactive area and a significantly improved electrochemical performance. The application of this novel electrochemical sensor for the sensitive quantification of traces of heavy metals has been demonstrated in combination with differential pulse anodic stripping voltammetry in model solutions.     

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.     

Structure of Framework Aluminum Lewis Sites and Perturbed Aluminum Atoms in Zeolites as Determined by 27Al{1H} REDOR (3Q) MAS NMR Spectroscopy and DFT/Molecular Mechanics

Zeolites are highly important heterogeneous catalysts. Besides Brønsted SiOHAl acid sites, also framework Al_FR Lewis acid sites are often found in their H‐forms. The formation of Al_FR Lewis sites in zeolites is a key issue regarding their selectivity in acid‐catalyzed reactions. The local structures of Al_FR Lewis sites in dehydrated zeolites and their precursors—“perturbed” Al_FR atoms in hydrated zeolites—were studied by high‐resolution MAS NMR and FTIR spectroscopy and DFT/MM calculations. Perturbed framework Al atoms correspond to (SiO)₃AlOH groups and are characterized by a broad ²⁷Al NMR resonance (δ_i=59–62 ppm, C_Q=5 MHz, and η=0.3–0.4) with a shoulder at 40 ppm in the ²⁷Al MAS NMR spectrum. Dehydroxylation of (SiO)₃AlOH occurs at mild temperatures and leads to the formation of Al_FR Lewis sites tricoordinated to the zeolite framework. Al atoms of these (SiO)₃Al Lewis sites exhibit an extremely broad ²⁷Al NMR resonance (δ_i≈67 ppm, C_Q≈20 MHz, and η≈0.1).