The Shape of Expansion Induced by a Line with Fast Diffusion in Fisher-KPP Equations

We establish a new property of Fisher-KPP type propagation in a plane, in the presence of a line with fast diffusion. We prove that the line enhances the asymptotic speed of propagation in a cone of directions. Past the critical angle given by this cone, the asymptotic speed of propagation coincides with the classical Fisher-KPP invasion speed. Several qualitative properties are further derived, such as the limiting behaviour when the diffusion on the line goes to infinity.     

Modular Curvature and Morita Equivalence

The curvature of the noncommutative torus \({T^2_\theta}\) (\({\theta \in \mathbb{R}{\setminus}\mathbb{Q}}\)) endowed with a noncommutative conformal metric has been the focus of attention of several recent works. Continuing the approach taken in the paper (Connes and Moscovici in J Am Math Soc 27:639–684, 2014) we extend the study of the curvature to twisted Dirac spectral triples constructed out of Heisenberg bimodules that implement the Morita equivalence of the C ^*-algebra \({A_\theta = C(T^2_\theta)}\) with other toric algebras \({A_{\theta'}=C(T^2_{\theta'})}\). In the enlarged context the conformal metric on \({T^2_\theta}\) is exchanged with an arbitrary Hermitian metric on the Heisenberg \({(A_\theta, A_{\theta'})}\)-bimodule E′ for which \({{\rm End}_{A_{\theta'}}(E') = A_\theta }\). We prove that the Ray-Singer log-determinant of the corresponding Laplacian, viewed as a functional on the space of all Hermitian metrics on E′, attains its extremum at the unique Hermitian metric whose corresponding connection has constant curvature. The gradient of the log-determinant functional gives rise to a noncommutative analogue of the Gaussian curvature. The genuinely new outcome of this paper is that the latter is shown to be independent of any Heisenberg bimodule E′ such that \({A_\theta = {\rm End}_{A_{\theta'}}(E')}\), and in this sense it is Morita invariant. To prove the above results we extend Connes’ pseudodifferential calculus to Heisenberg modules. The twisted version, which offers more flexibility even in the case of trivial coefficients, could potentially be applied to other problems in the elliptic theory on noncommutative tori. A noteworthy technical feature is that we systematize the computation of the resolvent expansion for elliptic differential operators on noncommutative tori to an extent which makes the (previously employed) computer assistance unnecessary.     

Flavonoids: hemisynthesis, reactivity, characterization and free radical scavenging activity

Phenolic compounds form one of the main classes of secondary metabolites. They display a large range of structures and they are responsible for the major organoleptic characteristics of plant-derived-foods and beverages, particularly color and taste properties and they also contribute to the nutritional qualities of fruits and vegetables. Phenolic compounds are also highly unstable compounds which undergo numerous enzymatic and chemical reactions during postharvest food storage and processing thus adding to the complexity of plant polyphenol composition. Among these compounds flavonoids constitute one of the most ubiquitous groups of all plant phenolics. Owing to their importance in food organoleptic properties and in human health, a better understanding of their structures, their reactivity and chemical properties in addition to the mechanisms generating them appears essential to predict and control food quality. The purpose of this work is an overview of our findings concerning the hemisynthesis, the reactivity and the enzymatic oxidation of some flavonoids and shed light on the mechanisms involved in some of these processes and the structures of the resulting products. The free radical scavenging activity of some of the synthesized compounds is also presented and a structure-activity relationship is discussed. The first part of this review concerns the synthesis and structural characterization of modified monomeric flavanols. The use of these compounds as precursor for the preparation of natural and modified dimeric procyanidin derivatives was then explored through different coupling reactions. The full characterization of the synthesized compounds was achieved by concerted use of NMR and ESI-MS techniques. The free radical scavenging activity of some of the synthesized compounds was investigated. The second part of this review concerns the enzymatic oxidation of several flavonols by Trametes versicolor laccase. Most of the major oxidation products have been isolated as pure compounds and their structures unambiguously established through spectroscopic methods. Correlation between the structure of the oxidation product and the substitution pattern of the starting materials allows mechanistic features of this transformation to be elucidated.     

Synthesis and NMR characterization of the cis and trans isomers of [Pt(II)(N9-adeH)2(pz)2] and X-ray crystallography of the trans isomer

The reaction of tetrapyrazine Pt(II) with adenine under basic conditions yielded two products both disubstituted by adenine and bound in all cases to the N-9 nitrogen of adenine. Crystals amenable to X-crystallographic analysis were obtained for one product which was consequently identified as trans-[Pt(II)(N9-adeH)2(pz)2](NO3)(4).H2O. The other product, though, was identified as the cis isomer based on extensive and comparative NMR structural studies whereby the two compounds were examined as both neutral and tetraprotonated species in solution. The major product of the reaction was unexpectedly the cis isomer, thus obtained in contrast to the trans effect, and the reason for this result is speculated on. Computational calculations using DFT at the B3LYP/TZVP-MARI-J level of theory provided the head-to-tail conformer as the overwhelmingly more stable species over the head-to-head conformer for both compounds whilst the trans product was found to be more stable than the cis. Thus the reaction does not follow a thermodynamic course and rather is kinetically controlled in concert with the speculated mode of reaction.     

SU-8 as a structural material for labs-on-chips and microelectromechanical systems

Since its introduction in the nineties, the negative resist SU-8 has been increasingly used in micro- and nanotechnologies. SU-8 has made the fabrication of high-aspect ratio structures accessible to labs with no high-end facilities such as X-ray lithography systems or deep reactive ion etching systems. These low-cost techniques have been applied not only in the fabrication of metallic parts or molds, but also in numerous other micromachining processes. Its ease of use has made SU-8 to be used in many applications, even when high-aspect ratios are not required. Beyond these pattern transfer applications, SU-8 has been used directly as a structural material for microelectromechanical systems and microfluidics due to its properties such as its excellent chemical resistance or the low Young modulus. In contrast to conventional resists, which are used temporally, SU-8 has been used as a permanent building material to fabricate microcomponents such as cantilevers, membranes, and microchannels. SU-8-based techniques have led to new low-temperature processes suitable for the fabrication of a wide range of objects, from the single component to the complete lab-on-chip. First, this article aims to review the different techniques and provides guidelines to the use of SU-8 as a structural material. Second, practical examples from our respective labs are presented.     

Carboxylic acid functional group analysis using constant neutral loss scanning-mass spectrometry

The present study describes the development of a new analytical technique for the functional group determination of the carboxylic moiety using atmospheric pressure chemical ionization-mass spectrometry (APCI-MS/MS) operated in the constant neutral loss scanning (CNLS) mode. Carboxylic groups were first derivatized into their corresponding methyl esters by reacting with BF₃/methanol mix and the reaction mixture was then directly injected into the APCI chamber. The loss of methanol (m/z = 32 amu) resulting from the fragmentation of the protonated methyl esters was then monitored. Applying this method together with a statistical approach to reference mixtures containing 31 different carboxylic acids at randomly calculated concentrations demonstrated its suitability for quantitative functional group measurements with relative standard deviations below 15% and a detection limit of 0.005 mmol L⁻¹. Its applicability to environmental matrices was also shown through the determination of carboxylic acid concentrations inside atmospheric aerosol samples. To the best of our knowledge, it is the first time that the tandem mass spectrometry was successfully applied to functional group analysis, offering great perspectives in the characterization of complex mixtures which are prevailing in the field of environmental analysis as well as in the understanding of the chemical processes occurring in these matrices.     

Disclosure of the imidazolium cation coordination and stabilization mode in ionic liquid stabilized gold(0) nanoparticles

A surface-enhanced Raman spectroscopy (SERS) study of imidazolium ionic liquid stabilized gold(0) nanoparticles (GNPs) furnished previously unknown knowledge about the coordination and stabilization mode of the imidazolium cation. GNPs were prepared by hydrazine reduction of a chloroauric acid solution in 1-triethylene glycol monomethyl ether-3-methylimidazolium methanesulfonate 2 as ether-functionalized room-temperature ionic liquid (RTIL). UV-vis spectroscopy showed the presence of GNP aggregates as absorptions extended to the NIR region. A parallel coordination mode for the imidazolium cation of RTIL 2 on the GNP surface was observed by SERS, which occurred without the simultaneous coordination of the 1-triethylene glycol monomethyl ether-functionality. Instead of this, the ether-functionality was directed away from the GNP surface and acted as steric barrier between the GNPs/GNP aggregates, thus preventing further aggregation. These new insights suggest that the imidazolium cation is responsible for electrosteric stabilization.     

Monopropionate analogues of DOTA4- and DTPA5-: kinetics of formation and dissociation of their lanthanide(III) complexes

The replacement of an acetate function of the macrocyclic DOTA4-(DO3A-Nprop4-) or the acyclic DTPA5- in terminal position (DTTA-Nprop5-) has been recently shown to result in a significant increase of the water exchange rate on the Gd3+ complexes, which makes these chelates potential contrast agents for MRI applications. Here, two novel and straightforward synthetic routes to H4DO3A-Nprop are described. Protonation constants of DO3A-Nprop4- and stability constants with several alkaline earth and transition metal ions have been determined by potentiometry. For each metal, the thermodynamic stability constant is decreased in comparison to the DOTA chelates. The formation reaction of LnDO3A-Nprop- complexes (Ln=Ce, Gd and Yb) proceeds via the rapid formation of a diprotonated intermediate and its subsequent deprotonation and rearrangement in a slow, OH- catalyzed process. The stability of the LnH2DO3A-Nprop* intermediates is similar to those reported for the corresponding DOTA analogues. The rate constants of the OH- catalyzed deprotonation step increase with decreasing lanthanide ion size, and are slightly higher than for DOTA complexes. The kinetic inertness of GdDTTA-Nprop2- was characterized by the rates of its exchange reactions with Zn2+ and Eu3+. The rate of the reaction between GdDTTA-Nprop2- and Zn2+ increases with Zn2+ concentration, while it is independent of pH, implying that the exchange takes place predominantly via direct attack of the metal ion on the complex. In the Eu3+ exchange, the rate decreases with increasing concentration of the exchanging ion which is accounted for by the transitional formation of a dinuclear GdDTTA-NpropEu+ species. The kinetic inertness of the monopropionate GdDTTA-Nprop2- is decreased in comparison to GdDTPA2-: all rate constants, characterizing the dissociation reaction via either proton- or metal-catalyzed pathways being higher by 1-2 orders of magnitude. Similarly, a study of the acid-catalyzed dissociation of the macrocyclic CeDO3A-Nprop- showed a partial loss of the kinetic inertness with regard to the tetraacetate derivative CeDOTA-.     

Limits of discrete series with infinitesimal character zero

For a connected linear semisimple Lie group , this paper considers those nonzero limits of discrete series representations having infinitesimal character 0, calling them totally degenerate. Such representations exist if and only if has a compact Cartan subgroup, is quasisplit, and is acceptable in the sense of Harish-Chandra.

Totally degenerate limits of discrete series are natural objects of study in the theory of automorphic forms: in fact, those automorphic representations of adelic groups that have totally degenerate limits of discrete series as archimedean components correspond conjecturally to complex continuous representations of Galois groups of number fields. The automorphic representations in question have important arithmetic significance, but very little has been proved up to now toward establishing this part of the Langlands conjectures.

There is some hope of making progress in this area, and for that one needs to know in detail the representations of under consideration. The aim of this paper is to determine the classification parameters of all totally degenerate limits of discrete series in the Knapp-Zuckerman classification of irreducible tempered representations, i.e., to express these representations as induced representations with nondegenerate data.

The paper uses a general argument, based on the finite abelian reducibility group attached to a specific unitary principal series representation of . First an easy result gives the aggregate of the classification parameters. Then a harder result uses the easy result to match the classification parameters with the representations of under consideration in representation-by-representation fashion. The paper includes tables of the classification parameters for all such groups .

     

Novel Route to Immobilize Metallocenes within Silica‐Based Supports: Investigation of a Nonhydrolytic Sol–Gel Process

A novel approach to metallocene catalyst heterogenization is presented. Supported metallocenes are obtained by metallation of indenyl‐modified silica produced by a nonhydrolytic sol–gel process. The catalytic activities for ethylene polymerization are rather high for supported systems and may reach 190 grams of polyethylene per gram of catalyst per hour per bar. The influence of the preparation and composition of these supported metallocene systems on ethylene polymerization and polyethylene characteristics are reported.

Possible structure of the indenyl‐modified silicas.