The methylation,oxidation and crystallographic characterization of imidazole derivatives

Compounds 2, 3 and 4 were synthesized and the crystal and molecular structures of 1 and 4 were determined. An hptlc technique for studying the methylation rate of 1 and the oxidation rate of 2 was applied.     

Ring opening of the molecular ion of 5(4H)-oxazolone

Quantum chemical calculations were carried out at several theoretical levels (semi-empirical, MNDO; ab initio, 3–21G SCF, 6–311G** SCF and DZP CISD) to investigate the ring-opening process of and the loss of CO from the molecular ion of 5(4H)-oxazolone. The ring-opening process is predicted to be slightly endothermic and the loss of CO from the open-ring molecular ion to be slightly exothermic. Detailed population analysis calculations suggest the weakening of the lactonic C? O bond in the closed-ring molecular ion and weak carbon—carbon and nitrogen—(formy)—carbon bonds in the open form. Both the open-ring molecular ion and the [M–CO]^+· ion are suggested to be of distonic type.     

A new family of representations of virtually free groups

We construct a new family of irreducible unitary representations of a finitely generated virtually free group Λ. We prove furthermore a general result concerning representations of Gromov hyperbolic groups that are weakly contained in the regular representation, thus implying that all the representations in this family can be realized on the boundary of Λ. As a corollary, we obtain an analogue of Herz majorization principle.     

Bi-stability of SUDR+K model of epidemics and test kits applied to COVID-19

Nonlinear Dynamics - Motivated by the many diverse responses of different countries to the COVID-19 emergency, here we develop a toy model of the dependence of the epidemics spreading on the...     

Thermal transformation of micro-crystalline cellulose in phosphoric acid

Use of crude oil derivatives such as diesel and gasoline is becoming unsuitable due to their detriment to environment and to the increasing worldwide energy demand which is driving crude oil reservoirs towards exhaustion. Replacement of diesel and gasoline with biofuels (i.e. biodiesel and bioethanol, respectively) is very desirable. In fact, biofuels are not only environmentally sustainable, but also potentially inexhaustible due to the large amounts of waste biomasses from which they can be retrieved. In the present study, a model compound (micro-crystalline cellulose) was dissolved in phosphoric acid and converted at 80 °C to glucose, thereby providing the possible substrate for fermentation to bioethanol. Results revealed that after 1 h heating, the reaction had the largest glucose yield as compared to similar studies done by using other acid catalysts. In addition, the temperature applied here was from 40 to 60 °C lower than those already reported in literature for acid-driven cellulose degradations. Phosphoric acid allowed both glucose and levulinic acid achievement. The latter is usually used to synthesize fuel additives, catalysts, solvents and herbicides, thereby enhancing the added value of the conversion of cellulose to glucose in phosphoric acid. Finally, ¹H T₁ NMR relaxometry showed its suitability to monitor cellulose degradation. The advantages of relaxomety are its quickness since only few minutes are needed to obtain relaxograms, and the possibility to use raw mixtures without the needing of sample preparation.     

Reactivity of asymmetric benzo-condensed diazines with nitrilimine dipoles in the 1,3-dipolar cycloaddition reactions

The reactivity of asymmetric benzo-condensed diazines in the 1,3-dipolar cycloaddition reactions with nitrilimines was investigated. The results demonstrated that, at variance with the symmetric quinoxaline, a certain grade of diastereoselectivity emerged. Moreover in the case of the 5-methylquinoxaline and quinazoline a mono-cycloadduct was obtained.     

Chemoenzymatic Synthesis of Fluorinated Cellodextrins Identifies a New Allomorph for Cellulose-Like Materials**

Understanding the fine details of the self-assembly of building blocks into complex hierarchical structures represents a major challenge en route to the design and preparation of soft-matter materials with specific properties. Enzymatically synthesised cellodextrins are known to have limited water solubility beyond DP9, a point at which they self-assemble into particles resembling the antiparallel cellulose II crystalline packing. We have prepared and characterised a series of site-selectively fluorinated cellodextrins with different degrees of fluorination and substitution patterns by chemoenzymatic synthesis. Bearing in mind the potential disruption of the hydrogen-bond network of cellulose II, we have prepared and characterised a multiply 6-fluorinated cellodextrin. In addition, a series of single site-selectively fluorinated cellodextrins was synthesised to assess the structural impact upon the addition of one fluorine atom per chain. The structural characterisation of these materials at different length scales, combining advanced NMR spectroscopy and microscopy methods, showed that a 6-fluorinated donor substrate yielded multiply 6-fluorinated cellodextrin chains that assembled into particles presenting morphological and crystallinity features, and intermolecular interactions, that are unprecedented for cellulose-like materials.     

Matchings in complete bipartite graphs and the r-Lah numbers

Czechoslovak Mathematical Journal - We give a graph theoretic interpretation of r-Lah numbers, namely, we show that the r-Lah number $${\left\lfloor {\matrix{n \cr k \cr } } \right\rfloor _r}$$...     

Enabling Circular Economy: The Overlooked Role of Inorganic Materials Chemistry

Circular economy is considered a new chance to build a more sustainable world from both the social and the economic point of view. In this Essay, the possible contribution of inorganic chemistry towards a smooth transition to circularity in inorganic materials design and production is discussed by adopting an interdisciplinary approach.