Quantum and Integral (Co)Bordisms in Partial Differential Equations

Characterizations of quantum bordisms and integral bordisms in PDEs by means of subgroups of usual bordism groups are given. More precisely, it is proved that integral bordism groups can be expressed as extensions of quantum bordism groups and these last are extensions of subgroups of usual bordism groups. Furthermore, a complete cohomological characterization of integral bordism and quantum bordism is given. Applications to particular important classes of PDEs are considered. Finally, we give a complete characterization of integral and quantum singular bordisms by means of some suitable characteristic numbers. Some examples of interesting PDEs which arise in physics are also considered where existence of solutions with change of sectional topology (tunnel effect) is proved. As an application, we relate integral bordism to the spectral term that represents the space of conservation laws for PDEs. This also gives a general method to associate in a natural way a Hopf algebra to any PDE.     

The ablation of quartz wall by SF6 under radiofrequency discharge

The behaviour of SF₆ in quartz and alumina tubes of a flow reactor capacitively coupled to a 35 MHz radiofrequency generator has been investigated at pressure of 20 torr, with power levels of 3.5÷5.5 cal cm^?3 sec^?1 and gas flow rates ranging between 0.1 and 2 1(STP) min^?1. A combination of gaschromatographic, mass spectrometric and infrared spectrophotometric techniques has shown the presence of SO₂F₂, SOF₄, SOF₂, SiF₄, F₂, O₂ together with unreacted SF₆ in the discharge products.A detailed quantitative investigation of the effluent products and of their concentration profiles versus space time and power is presented and a general mechanism for the ablation process of the quartz wall is suggested.     

Erratum to: The linkup of mono-elemental solutions to the SI using INAA: a measurement procedure and the achievable uncertainty

Journal of Radioanalytical and Nuclear Chemistry -     

Characterisation of the different hands in the composition of a 14th century breviary by means of portable XRF analysis and complementary techniques

A 14th‐century breviary known as Breviario di San Michele della Chiusa, produced at the disposal of the monks of Sacra di San Michele abbey (near Turin, Italy) has been analysed in order to identify the different authors who contributed in its making. The study aimed at revealing how many scribes composed the text and the musical notations and how many artists worked for miniatures and for the decorations of initials. All inks and decorative features have been analysed by means of portable X‐ray fluorescence spectrometry for determining elemental distribution and by means of ultraviolet–Visible diffuse reflectance spectrophotometry with optic fibres and spectrofluorimetry for identifying colourants. The results on non‐invasive measurements highlighted that at least 11 persons (six scribes for the text, two scribes for the musical notations, two artists for initials and filigrees and one artist for the full‐page miniature at f. 208v) were at work at the Breviario. Moreover, the black inks used for text and notes have an anomalous composition, being iron gall inks with a larger than usual amount of zinc, possibly as a consequence of the use of vitriols made from goslarite; this suggests that the scribes could come from Northern Europe. The presence of traces of bismuth in blue paints also suggested the provenance of azurite from Central or Northern Europe. Copyright © 2017 John Wiley & Sons, Ltd.     

Rotational spectra of rare isotopic species of fluoroiodomethane: determination of the equilibrium structure from rotational spectroscopy and quantum-chemical calculations

Supported by accurate quantum-chemical calculations, the rotational spectra of the mono- and bi-deuterated species of fluoroiodomethane, CHDFI and CD(2)FI, as well as of the (13)C-containing species, (13)CH(2)FI, were recorded for the first time. Three different spectrometers were employed, a Fourier-transform microwave spectrometer, a millimeter/submillimter-wave spectrometer, and a THz spectrometer, thus allowing to record a huge portion of the rotational spectrum, from 5 GHz up to 1.05 THz, and to accurately determine the ground-state rotational and centrifugal-distortion constants. Sub-Doppler measurements allowed to resolve the hyperfine structure of the rotational spectrum and to determine the complete iodine quadrupole-coupling tensor as well as the diagonal elements of the iodine spin-rotation tensor. The present investigation of rare isotopic species of CH(2)FI together with the results previously obtained for the main isotopologue [C. Puzzarini, G. Cazzoli, J. C. Lo?pez, J. L. Alonso, A. Baldacci, A. Baldan, S. Stopkowicz, L. Cheng, and J. Gauss, J. Chem. Phys. 134, 174312 (2011); G. Cazzoli, A. Baldacci, A. Baldan, and C. Puzzarini, Mol. Phys. 109, 2245 (2011)] enabled us to derive a semi-experimental equilibrium structure for fluoroiodomethane by means of a least-squares fit procedure using the available experimental ground-state rotational constants together with computed vibrational corrections. Problems related to the missing isotopic substitution of fluorine and iodine were overcome thanks to the availability of an accurate theoretical equilibrium geometry (computed at the coupled-cluster singles and doubles level augmented by a perturbative treatment of triple excitations).     

Instrumental neutron activation analysis of an enriched 28Si single-crystal

The determination of the Avogadro constant plays a key role in the redefinition of the kilogram in terms of a fundamental constant. The present experiment makes use of a silicon single-crystal highly enriched in ²⁸Si that must have a total impurity mass fraction smaller than a few parts in 10⁹. To verify this requirement, we previously developed a relative analytical method based on neutron activation for the elemental characterization of a sample of the precursor natural silicon crystal WASO 04. The method is now extended to fifty-nine elements and applied to a monoisotopic ²⁸Si single-crystal that was grown to test the achievable enrichment. Since this crystal was likely contaminated, this measurement tested also the detection capabilities of the analysis. The results quantified contaminations by Ge, Ga, As, Tm, Lu, Ta, W and Ir and, for a number of the detectable elements, demonstrated that we can already reach the targeted 1 ng/g detection limit.