Singularity Formation in Fractional Burgers’ Equations

The formation of singularities in finite time in nonlocal Burgers’ equations, with time-fractional derivative, is studied in detail. The occurrence of finite-time singularity is proved, revealing the underlying mechanism, and precise estimates on the blowup time are provided. The employment of the present equation to model a problem arising in job market is also analyzed.

     

Post‐Synthetic Ligand Exchange in Zirconium‐Based Metal–Organic Frameworks: Beware of The Defects!

Post‐synthetic ligand exchange in the prototypical zirconium‐based metal–organic framework (MOF) UiO‐66 was investigated by in situ solution ¹H NMR spectroscopy. Samples of UiO‐66 having different degrees of defectivity were exchanged using solutions of several terephthalic acid analogues in a range of conditions. Linker exchange only occurred in defect‐free UiO‐66, whereas monocarboxylates grafted at defect sites were found to be preferentially exchanged with respect to terephthalic acid over the whole range of conditions investigated. A 1:1 exchange ratio between the terephthalic acid analogue and modulator was observed, providing evidence that the defects had missing‐cluster nature. Ex situ characterisation of the MOF powders after exchange corroborated these findings and showed that the physical‐chemical properties of the MOF depend on whether the functionalisation occurs at defective sites or on the framework.     

Classification of Bertini's Series of Varieties of Dimension Less than or Equal to Four

In this paper I give a classification of irreducible projective varieties of dimension less than or equal to four, according to a new classification scheme. No assumption is made about singularities.     

Symmetrization and norm of the Hardy-Littlewood maximal operator on Lorentz and Marcinkiewicz spaces

We prove that when a function on the real line is symmetricallyrearranged, the distribution function of its uncentered Hardy–Littlewoodmaximal function increases pointwise, while it remains unchangedonly when the function is already symmetric. Equivalently, if is the maximal operator and the symmetrization, then f(x)f(x)for every x, and equality holds for all x if and only if, upto translations, f(x) = f(x) almost everywhere. Using theseresults, we then compute the exact norms of the maximal operatoracting on Lorentz and Marcinkiewicz spaces, and we determineextremal functions that realize these norms.     

Fully reversible guest exchange in tetraphosphonate cavitand complexes probed by fluorescence spectroscopy

We report here the monitoring of reversible guest inclusion in phosphonate cavitands through a large increase in luminescence intensity caused by the modulation of the exoergonicity of an electron-transfer reaction.     

Unraveling the dynamics of the C(3P,1D) + C2H2 reactions by the crossed molecular beam scattering technique

A detailed investigation of the dynamics of the reactions of ground- and excited-state carbon atoms, C(3P) and C(1D), with acetylene is reported over a wide collision energy range (3.6-49.1 kJ mol-1) using the crossed molecular beam (CMB) scattering technique with electron ionization mass spectrometric detection and time-of-flight (TOF) analysis. We have exploited the capability of (a) generating continuous intense supersonic beams of C(3P, 1D), (b) crossing the two reactant beams at different intersection angles (45, 90, and 135 degrees ) to attain a wide range of collision energies, and (c) tuning the energy of the ionizing electrons to low values (soft ionization) to suppress interferences from dissociative ionization processes. From angular and TOF distribution measurements of products at m/z=37 and 36, the primary reaction products of the C(3P) and C(1D) reactions with C2H2 have been identified to be cyclic (c)-C3H + H, linear (l)-C3H + H, and C3 + H2. From the data analysis, product angular and translational energy distributions in the center-of-mass (CM) system for both the linear and cyclic C3H isomers as well as the C3 product from C(3P) and for l/c-C3H and C3 from C(1D) have been derived as a function of collision energy from 3.6 to 49.1 kJ mol-1. The cyclic/linear C3H ratio and the C3/(C3 + c/l-C3H) branching ratios for the C(3P) reaction have been determined as a function of collision energy. The present findings have been compared with those from previous CMB studies using pulsed beams; here, a marked contrast is noted in the CM angular distributions for both C3H- and C3-forming channels from C(3P) and their trend with collision energy. Consequently, the interpretation of the reaction dynamics derived in the present work contradicts that previously proposed from the pulsed CMB studies. The results have been discussed in the light of the available theoretical information on the relevant triplet and singlet C3H2 ab initio potential energy surfaces (PESs). In particular, the branching ratios for the C(3P) + C2H2 reaction have been compared with the available theoretical predictions (approximate quantum scattering calculations and quasiclassical trajectory calculations on ab initio triplet PESs and, very recent, statistical calculations on ab initio triplet PESs as well as on ab initio triplet/singlet PESs including nonadiabatic effects, that is, intersystem crossing). While the experimental branching ratios have been corroborated by the statistical predictions, strong disagreement has been found with the results of the dynamical calculations. The astrophysical implications of the present results have been noted.     

Water droplets as template for next-generation self-assembled poly-(etheretherketone) with cardo membranes

Next generation PEEK-WC membranes have been fabricated by using an innovative self-assembly technique. Patterned architectures have been achieved via a solvent-reduced and water-assisted process, resulting in honeycomb packed geometry. The membranes exhibit monodisperse pores with size and shape comparable to those left by templating water droplets. Influencing factors for the formation of self-assembled poly-(etheretherketone) with Cardo [PEEK-WC] membranes have been evaluated, identifying the critical parameters for nucleation, growth, and propagation of the droplet-mobile arrays through the overall films. Structure-transport relationships have been discussed according to the results achieved from the implementation of membrane distillation processes, yielding indication about the suitability of self-assembled PEEK-WC films to work as interfaces in contactor operations.     

Myoglobin modification by enzyme-generated dopamine reactive species

The generation of reactive quinone species (DAQ) from oxidation of dopamine (DA) is involved in neurodegenerative pathologies like Parkinson's disease (A. Borta, G. U. H?glinger, J. Neurochem. 2007, 100, 587-595). The oxidation of DA to DAQ can occur either in a single two-electron process or in two consecutive one-electron steps, through semiquinone radicals, giving rise to different patterns of reactions. The former type of reaction can be promoted by tyrosinase, the latter by peroxidases in the presence of H(2)O(2), which can be formed under oxidative stress conditions. Both enzymes were employed for the characterization of the thiol-catechol adducts formed by reaction of DA and cysteine or glutathione, and for the identification of specific amino acid residues modified by DAQs in two representative target proteins, human and horse heart myoglobin. Our results indicate that the cysteinyl-DA adducts are formed from the same quinone intermediate independently of the mechanism of DA oxidation, and that the hallmark of a radical mechanism is the formation of the cystine dimer. The reactivity of quinone species also controls the DA-promoted derivatization of histidine residues in proteins. However, for the modification of the cysteine residue in human myoglobin, a radical intramolecular mechanism has been proposed, in which the protein acts both as the catalyst and target of the reaction. Most importantly, the modification of myoglobins through DAQ linkages, and in particular by DA oligomers, has dramatic effects on their stability, as it induces protein unfolding and incorporation into insoluble melanic precipitates.