Equivalent forms of Levi condition

In this paper we consider hyperbolic differential operators with characteristic roots of constant multiplicity and we prove the equivalence of some conditions, called Levi conditions, for the correctness of the Cauchy problem inC ^∞ and in Gevrey classes.

---

Sommario In questo articolo prendiamo in considerazione operatori differenziali iperbolici con caratteristiche di molteplicità costante e dimostriamo l’equivalenza di alcune condizioni, note come condizioni di Levi, necessarie e sufficienti per la buona positura del problema di Cauchy nelle classiC ^∞ e Gevrey.

     

Comparison between CP/MAS 13C-NMR and pyrolysis-GC/MS in the structural characterization of humins and humic acids of soil and sediments

The chemical structure of humins (HUs) and humic acids (HAs) of terrestrial and marine environments was investigated by cross-polarization magic angle spinning ¹³C-nuclear magnetic resonance spectroscopy (CP/ MAS ¹³C-NMR) and pyrolysis-gas chromatography/mass spectrometry (Py-GC/MS). Samples of HUs and HAs were obtained from sediments of the Adriatic Sea, the Lagoon of Ravenna (Adriatic Sea) and the Bubano Lake as well as from an agricultural soil. HUs displayed pyrograms and NMR spectra different from those of related HAs. According to NMR spectra HUs were more aliphatic and contained fewer carboxyl groups than HAs, while pyrolysates of HUs were characterized by higher levels of products arising from carbohydrates and lower levels of lignin methoxyphenols with respect to HAs. The relative content of paraffinic carbons determined by NMR was in good agreement with the relative abundance of unbranched aliphatic hydrocarbons released by pyrolysis. Both techniques evidenced the importance of polymethylene structures in HUs. Received: 5 January 1998 / Revised: 24 March 1998 / Accepted: 25 March 1998     

Pyrolysis/gas chromatography/mass spectrometry of asphaltene fractions

Two n-heptane-precipitated asphaltene samples, characterized by elemental analysis and nuclear magnetic resonance spectrometry, were fractionated according to relative molecular size by gel permeation chromatography (GPC). Both the whole asphaltene samples and their fractions were analysed by pyrolysis/gas chromatography/mass spectrometry. The data obtained from the pyrograms (average side-chain length, aromaticity index, sulphur compounds vs. aliphatic compounds, presence of SO₂ and CO₂) demonstrated that, in the case of asphaltenes, GPC fractionation results in the separation of different chemical structures ranging from lower molecular mass, highly aromatic and polar compounds to higher molecular mass, less polar and aromatic compounds.     

Img2Mol – accurate SMILES recognition from molecular graphical depictions

The automatic recognition of the molecular content of a molecule''s graphical depiction is an extremely challenging problem that remains largely unsolved despite decades of research. Recent advances in neural machine translation enable the auto-encoding of molecular structures in a continuous vector space of fixed size (latent representation) with low reconstruction errors. In this paper, we present a fast and accurate model combining deep convolutional neural network learning from molecule depictions and a pre-trained decoder that translates the latent representation into the SMILES representation of the molecules. This combination allows us to precisely infer a molecular structure from an image. Our rigorous evaluation shows that Img2Mol is able to correctly translate up to 88% of the molecular depictions into their SMILES representation. A pretrained version of Img2Mol is made publicly available on GitHub for non-commercial users.

The automatic recognition of the molecular content of a molecule''s graphical depiction is an extremely challenging problem that remains largely unsolved despite decades of research.