Determination of trace impurities in aluminum nitride by direct solid sampling graphite furnace atomic absorption spectrometry

The trace impurities Cr, Cu, Fe, K, Mn, Sb and Zn were determined in powdered aluminum nitride by direct solid sampling graphite furnace atomic absorption spectrometry using a ZEEnit 60 atomic absorption spectrometer. This spectrometer features inverse Zeeman-effect background correction and a variable magnetic field enabling measurements in two sensitivity modes over a concentration range of three orders of magnitude. The measurement sensitivity can be adjusted to the analyte concentration in the sample. The use of chemical modifiers was not necessary. Calibration was carried out by means of calibration curves obtained with aqueous standard solutions. Accuracy was checked mainly by comparison of the results with those obtained by instrumental and radiochemical neutron activation analysis whereby, excluding the results for potassium, no significant differences were found by carrying out the t-test at the significance level 0.05. The limits of detection were between 0.05 ng g⁻¹ (Zn) and 80 ng g⁻¹ (Fe) and the relative standard deviations below 11 %. With the proposed method, up to ten measurement cycles can be carried out in one hour.     

Tjon Lines and Scaling Limit in Four-Body Systems

The fixed-slope correlation between tetramer and trimer binding energies, observed by Tjon in the context of nuclear physics, is mainly a manifestation of the dominance of the two-nucleon force in the nuclear potential, which makes the four-body scale on the order of the three-body one. In a more general four-boson case, the correlation between tetramer and trimer binding energies has a non-fixed slope, which expresses the dependence on the new scale. The associated scaling function generates a family of Tjon lines. This conclusion relies on a recent study with weakly-bound four identical bosons, within a renormalized zero-range Faddeev-Yakubovsky formalism.     

New lower bound for the Hilbert number in piecewise quadratic differential systems

We study the number of limit cycles bifurcating from a piecewise quadratic system. All the differential systems considered are piecewise in two zones separated by a straight line. We prove the existence of 16 crossing limit cycles in this class of systems. If we denote by $H_p(n)$ the extension of the Hilbert number to degree n piecewise polynomial differential systems, then $H_p(2)\ge 16$. As fas as we are concerned, this is the best lower bound for the quadratic class. Moreover, in the studied cases, all limit cycles appear nested bifurcating from a period annulus of a isochronous quadratic center.     

Range Corrections to Universal Tetramer Properties

The universal properties of weakly-bound tetramers close to the scaling limit are investigated by solving a subtracted set of Faddeev–Yakubovsky (FY) equations for identical bosons with a zero-range interaction. The solution demands a four-body scale independent of the trimer properties. Furthermore, the effect of a finite effective range is introduced in the FY equations, which we show produces results that are distinct from the scale variation. In particular range effects to two universal scaling functions for the tetramers are investigated. The correlation between successive tetramer energies corresponding to states within two Efimov trimer energies, proposed before and studied close to the unitary limit; and the correlation between the position of the four-atom recombination peaks. In this case, we found a shift in the scaling function due to the range, which can be associated to the shift of the data found for caesium atoms, with respect to zero-range calculations, due to a nonvanishing range in the actual experimental setups.     

Asymptotics of Selberg-like integrals by lattice path counting

We obtain explicit expressions for positive integer moments of the probability density of eigenvalues of the Jacobi and Laguerre random matrix ensembles, in the asymptotic regime of large dimension. These densities are closely related to the Selberg and Selberg-like multidimensional integrals. Our method of solution is combinatorial: it consists in the enumeration of certain classes of lattice paths associated to the solution of recurrence relations.     

Lorentz Violation and Topologically Trapped Fermions in 2+1 Dimensions

The full spectrum of two‐dimensional fermion states in a scalar soliton trap with a Lorentz breaking background is investigated in the context of graphene, where the Lorentz symmetry should not be strictly valid. The field theoretical model with Lorentz breaking terms represents Dirac electrons in one valley and in a scalar field background. The Lorentz violation comes from the difference between the Dirac electron and scalar mode velocities, which should be expected when modelling the electronic and lattice excitations in graphene. Here, only one Lorentz‐violating parameter is considered, belonging to the scalar sector. The analytical methods developed in the context of 1+1 field theories are extended to explore the effect of the Lorentz symmetry breaking in the charge carrier density of two‐dimensional materials in the presence of a domain wall with a kink profile. The width and the depth of the trapping potential from the kink is controlled by the Lorentz violating term, which is reflected analytically in the band structure and properties of the trapped states. These findings enlarge previous studies of the edge states obtained with domain wall and in strained graphene nanoribbon in a chiral gauge theory.     

An Alexandrov–Fenchel-type inequality for hypersurfaces in the sphere

We find a monotone quantity along the inverse mean curvature flow and use it to prove an Alexandrov–Fenchel-type inequality for strictly convex hypersurfaces in the n-dimensional sphere, \(n \ge 3\).     

Cd1-xMgxTe semiconductor nanocrystal alloys: Synthesis,preparation of nanocomposites with graphene-based materials,and electrochemical detection of lidocaine and epinephrine

Microchimica Acta - This work describes the synthesis of a glutathione-capped Cd1-xMgxTe semiconductor nanocrystal alloy in aqueous solution. The effects of reaction time and Cd:Mg molar proportion...     

Characterization of Gasoline by Raman Spectroscopy with Chemometric Analysis

A rapid Raman spectroscopy protocol is reported to classify gasoline according to its distributor and to identify and quantify common adulterants. Gasoline from three distributors was collected from 19 stations in São Paulo, Brazil. Principal component analysis (PCA) showed specific clusters for each distributor, and partial least squares discriminant analysis (PLS-DA) correctly identified the origin of the samples. To evaluate the technique for the identification and quantification of the adulterants, authentic samples from each distributor were fortified at levels from 2.5 up to 25.0% (v/v) using ethanol, methanol, toluene, and turpentine to obtain 120 altered samples. PCA showed clear separation among the samples with the adulterants and PLS-DA precisely identified the adulterants (478 in 480 predictions by cross-validation), irrespective of the distributor and the concentration. One classification model was used to characterize all distributors. To quantify the adulterants, 36 multivariate calibration models were constructed using partial least squares (PLS), interval PLS, and PLS genetic algorithm for each distributor and for each adulterant. Cross-validation errors of less than 5.0% were obtained for all adulterants regardless of the distributor. Raman spectroscopy and multivariate analysis were shown to be powerful for rapid and inexpensive for the characterization of gasoline origin and the identification and quantification of common adulterants.