A generalization of Knopp’s Observation on Ramanujan’s tau-function

The Ramanujan Journal - We establish a vast generalization of an observation made by Marvin Knopp half a century ago concerning the nonvanishing of Ramanujan’s tau-function.     

Advances in the computational analysis of SARS-COV2 genome

Nonlinear Dynamics - Given a data-set of Ribonucleic acid (RNA) sequences we can infer the phylogenetics of the samples and tackle the information for scientific purposes. Based on current data and...     

Adaptive mesh refinement and coarsening for aerodynamic flow simulations

A new mesh refinement technique for unstructured grids is discussed. The new technique presents the important advantage of maintaining the original grid skewness, thanks to the capability of handling hanging nodes. The paper also presents an interpretation of MacCormack's method in an unstructured grid context. Results for a transonic convergent–divergent nozzle, for a convergent nozzle with a supersonic entrance and for transonic flow over a NACA 0012 airfoil are presented and discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

The effect of mechanochemical activation on the reactivity in the MgO–Al2O3–SiO2 system

Samples of the MgO–Al₂O₃–SiO₂ ternary system, constituted by 28.5 mol% ofMgO, 28.5 mol% of Al₂O₃ and 43mol%of SiO₂, were activated in a roll mill and calcined at different temperatures. The influence of the grinding time, the used SiO₂ precursor and activation medium, furthermore the mass ratio between the powdered sample and zirconia cylinders was investigated on the reactivity of the MgO–Al₂O₃–SiO₂ ternary system. FTIR spectra and the X-ray powder diffraction patterns indicates the formation of Mg(OH)₂ at 393 K, of forsterite (MgSi₂O₅) and enstatite (MgSiO₃) at 1223 K and of spinel (MgAl₂O₄) between 1223 and 1523 K in some samples. The presence of cordierite (Mg₂Al₂Si₅O₁₈) was observed at 1523 K, a reaction pathway concerning its formation was proposed.     

Automotive Gasoline Quality Analysis by Gas Chromatography: Study of Adulteration

Summary The addition of organic solvents (light aliphatic, heavy aliphatic and aromatic hydrocarbons) in Brazilian gasoline is unfortunately very frequent, and this illicit practice impares gasoline quality. Gas chromatography (GC) and gas chromatography coupled to mass spectrometry (GC-MS) analyses can be used as a procedure to improve the detection of adulterated gasoline. The results showed that adulterated samples and also the type of organic solvent used in adulteration can be detected by comparison of chromatographic profiles (standard samples versus adulterated samples). However, a single GC analysis can detect an adulterated gasoline, and so decrease the number of adulterated samples approved as presenting good quality.     

Real-Time Monitoring Polymerization Reactions Using Dipolar Echoes in 1H Time Domain NMR at a Low Magnetic Field

¹H time domain nuclear magnetic resonance (¹H TD-NMR) at a low magnetic field becomes a powerful technique for the structure and dynamics characterization of soft organic materials. This relies mostly on the method sensitivity to the ¹H-¹H magnetic dipolar couplings, which depend on the molecular orientation with respect to the applied magnetic field. On the other hand, the good sensitivity of the ¹H detection makes it possible to monitor real time processes that modify the dipolar coupling as a result of changes in the molecular mobility. In this regard, the so-called dipolar echoes technique can increase the sensitivity and accuracy of the real-time monitoring. In this article we evaluate the performance of commonly used ¹H TD-NMR dipolar echo methods for probing polymerization reactions. As a proof of principle, we monitor the cure of a commercial epoxy resin, using techniques such as mixed-Magic Sandwich Echo (MSE), Rhim Kessemeier—Radiofrequency Optimized Solid Echo (RK-ROSE) and Dipolar Filtered Magic Sandwich Echo (DF-MSE). Applying a reaction kinetic model that supposes simultaneous autocatalytic and noncatalytic reaction pathways, we show the analysis to obtain the rate and activation energy for the epoxy curing reaction using the NMR data. The results obtained using the different NMR methods are in good agreement among them and also results reported in the literature for similar samples. This demonstrates that any of these dipolar echo pulse sequences can be efficiently used for monitoring and characterizing this type of reaction. Nonetheless, the DF-MSE method showed intrinsic advantages, such as easier data handling and processing, and seems to be the method of choice for monitoring this type of reaction. In general, the procedure is suitable for characterizing reactions involving the formation of solid products from liquid reagents, with some adaptations concerning the reaction model.     

First-principles studies of zigzag pristine boron nitride nanotubes doped with one iron atom

Interaction of one iron atom with pristine zigzag boron nitride nanotubes with different diameters, ranging from (8,0) to (12,0), have been investigated using density functional theory calculations. Departing from four initial configurations, considering each of them interacting with the tubes’ walls either from inside or outside, we have analyzed the adsorbate migration to the most favorable positions together with the related binding energies and the equilibrium distances as well as the electronic structure of the final systems. It was observed that the smaller the radius of the tube the lower is the binding energy for all studied structures, and also that the inner configuration is more stable than the outer one for small radius. For the preferred position for the iron atom, it was seen that it varies according to the starting configuration and that the iron-first-nitrogen-neighbor bond length works as a constraint in determining the most favorable position for the adsorbate. Finally, for the electronic structure, it was observed that the presence of the dopant introduces localized levels at the band gap of the nanotubes and that those levels are mostly related to the orbitals 3d and 4s of the iron atom. For the inside case, as a consequence of higher hybridization and a confinement effect, the gap closure is more pronounced for small diameter tubes. For all studied structures, it was observed a net-spin-polarization equal to 4 μ _B.