Noether's Theorem on Surfaces

In this article we prove a version of Noether's Theorem (of Calculus of Variations) which is valid for a general regular (compact) surface. As a special feature, the Lie group of transformations is allowed to act on the Cartesian product of the surface and the functional space. Additionally, we apply the Theorem to a problem in Classical Differential Geometry of surfaces. The given application is actually an example showing how Noether's Theorem can be used to construct invariant properties of the solutions to variational problems defined on surfaces, or equivalently, of the solutions to the associated Euler-Lagrange equations resulting from them.     

Optimized Synthesis of Silver Nanoparticles by Factorial Design with Application for the Determination of Melamine in Milk

A colorimetric method based on silver nanoparticles was developed for the determination of melamine in milk. Silver nanoparticles were synthesized without any stabilizer, using sodium borohydride as the reducing agent. Optimization of the variables for the formation of the nanoparticles was performed by factorial design, resulting in stable colloidal silver nanoparticles with a mean diameter of 14.0?±?2.7?nm. Spectrophotometric measurements performed at 475?nm showed a linear range from 0.033 to 1.50?mg?L^?1 of melamine with limits of detection and quantification of 0.009 and 0.031?mg?L^?1, respectively. The method provided highly sensitive determination of melamine in milk.     

Understanding the Deactivation Pathways of Iridium(III) Pyridine-Carboxiamide Catalysts for Formic Acid Dehydrogenation

The degradation pathways of highly active [Cp*Ir(κ²-N,N-R-pica)Cl] catalysts (pica=picolinamidate; 1 R=H, 2 R=Me) for formic acid (FA) dehydrogenation were investigated by NMR spectroscopy and DFT calculations. Under acidic conditions (1 equiv. of HNO₃), 2 undergoes partial protonation of the amide moiety, inducing rapid κ²-N,N to κ²-N,O ligand isomerization. Consistently, DFT modeling on the simpler complex 1 showed that the κ²-N,N key intermediate of FA dehydrogenation ( I_NH ), bearing a N-protonated pica, can easily transform into the κ²-N,O analogue ( I_NH2 ; ΔG^≠≈11 kcal mol⁻¹, ΔG ≈−5 kcal mol⁻¹). Intramolecular hydrogen liberation from I_NH2 is predicted to be rather prohibitive (ΔG^≠≈26 kcal mol⁻¹, ΔG≈23 kcal mol⁻¹), indicating that FA dehydrogenation should involve mostly κ²-N,N intermediates, at least at relatively high pH. Under FA dehydrogenation conditions, 2 was progressively consumed, and the vast majority of the Ir centers (58 %) were eventually found in the form of Cp*-complexes with a pyridine-amine ligand. This likely derived from hydrogenation of the pyridine-carboxiamide via a hemiaminal intermediate, which could also be detected. Clear evidence for ligand hydrogenation being the main degradation pathway also for 1 was obtained, as further confirmed by spectroscopic and catalytic tests on the independently synthesized degradation product 1 c . DFT calculations confirmed that this side reaction is kinetically and thermodynamically accessible.     

Comparison between preparative methodologies of nanostructured carbon nitride and their use as selective photocatalysts in water suspension

Carbon nitride photocatalysts have been prepared by different methodologies, such as chemical ultrasonic irradiation (sonochemical treatment), hydrothermal and ball milling and thermoexfoliation, and have been used for the selective oxidation of 5-hydroxymethyl-2-furaldehyde (HMF) to form 2,5-furandicarboxyaldehyde (FDC) in water suspension both under UV and natural solar irradiation. The physico-chemical features of the photocatalysts have been studied by X-ray diffraction, infrared spectroscopy, UV–Vis diffuse reflectance spectroscopy, photoluminescence spectroscopy, scanning electron microscopy, and specific surface area measurements. The results indicate that exfoliation of carbon nitrides can increase the conversion of HMF and the selectivity to FDC. In particular, samples exfoliated by both thermal and acidic ultrasonic irradiation treatments showed the best photocatalytic performance.     

Modeling Transverse Relative Locality

We investigate some aspects of relativistic classical theories with “relative locality”, in which pairs of events established to be coincident by nearby observers may be described as non-coincident by distant observers. While previous studies focused mainly on the case of longitudinal relative locality, where the effect occurs along the direction connecting the distant observer to the events, we here focus on transverse relative locality, in which instead the effect is found in a direction orthogonal to the one connecting the distant observer to the events. Our findings suggest that, at least for theories of free particles, transverse relative locality is as significant as longitudinal relative locality both conceptually and quantitatively. And we observe that “dual gravity lensing” can be viewed as one of two components of transverse relative locality. We also speculate about a type of spacetime noncommutativity for which transverse relative locality could be particularly significant.