Structures,Bonding Analyses and Reactivity of a Dicationic Digallene and Diindene Mimicking trans-bent Ditetrylenes

The reaction of bisdicyclohexylphosphinoethane (dcpe) and the subvalent M^I sources [M^I(PhF)₂][pf] (M=Ga⁺, In⁺; [pf]⁻=[Al(OR^F)₄]⁻; R^F=C(CF₃)₃) yielded the salts [{M(dcpe)}₂][pf]₂, containing the first dicationic, trans-bent digallene and diindene structures reported so far. The non-classical M^I⇆M^I double bonds are surprisingly short and display a ditetrylene-like structure. The bonding situation was extensively analyzed by quantum chemical calculations, QTAIM (Quantum Theory of Atoms in Molecules) and EDA-NOCV (Energy Decomposition Analysis with the combination of Natural Orbitals for Chemical Valence) analyses and is compared to that in the isoelectronic and isostructural, but neutral digermenes and distannenes. The dissolved [{Ga(dcpe)}₂]²⁺([pf]⁻)₂ readily reacts with 1-hexene, cyclooctyne, diphenyldisulfide, diphenylphosphine and under mild conditions at room temperature. This reactivity is analyzed and rationalized.     

Stationary Increments Harmonizable Stable Fields: Upper Estimates on Path Behaviour

Studying sample path behaviour of stochastic fields/processes is a classical research topic in probability theory and related areas such as fractal geometry. To this end, many methods have been developed for a long time in Gaussian frames. They often rely on some underlying “nice” Hilbertian structure and can also require finiteness of moments of high order. Therefore, they can hardly be transposed to frames of heavy-tailed stable probability distributions. However, in the case of some linear non-anticipative moving average stable fields/processes, such as the linear fractional stable sheet and the linear multi-fractional stable motion, rather new wavelet strategies have already proved to be successful in order to obtain sharp moduli of continuity and other results on sample path behaviour. The main goal of our article is to show that, despite the difficulties inherent in the frequency domain, such kind of a wavelet methodology can be generalized and improved, so that it also becomes fruitful in a general harmonizable stable setting with stationary increments. Let us point out that there are large differences between this harmonizable setting and the moving average stable one. The real-valued harmonizable stable stochastic field X on which we focus is defined on \(\mathbb {R}^d\) through an arbitrary spectral density belonging to a general and wide class of functions. First, we introduce a wavelet-type random series representation of X and express it as the finite sum \(X=\sum _\eta X^\eta \), where the fields \(X^\eta \) are called the \(\eta \)-frequency parts, since they extend the usual low-frequency and high-frequency parts. Moreover, we show the continuity of the sample paths of the \(X^\eta \)’s and X; also, we discuss the existence and continuity of their partial derivatives of an arbitrary order. Thereafter, we obtain several almost sure upper estimates related to: (a) the anisotropic behaviour of generalized directional increments of the \(X^\eta \)’s and X, on an arbitrary fixed compact cube of \(\mathbb {R}^d\); (b) the behaviour at infinity of the \(X^\eta \)’s, of X, and of their partial derivatives, when they exist. We mention that all the results on sample paths obtained in the article are valid on the same event of probability 1; furthermore, this event is “universal”, in the sense that it does not depend, in any way, on the spectral density associated with X.     

Oscillations in the height of the Yule tree and application to the binary search tree

For a particular case of a branching random walk with lattice support, namely the Yule branching random walk, we prove that the distribution of the centred maximum oscillates around a distribution corresponding to a critical travelling wave in the following sense: there exist continuous functions and such that: where and is the height of the Yule tree. We also shows that similar oscillations occur for , when f is in a large class of functions. This process is classically related to the binary search tree, thus yielding analogous results for the height and for the saturation level of the binary search tree. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 90–120, 2017     

Visible Multiphoton Dissociation of Chromophore-Tagged Peptides

The visible photodissociation mechanisms of QSY7-tagged peptides of increasing size have been investigated by coupling a mass spectrometer and an optical parametric oscillator laser beam. The experiments herein consist of energy resolved collision- and laser-induced dissociation measurements on the chromophore-tagged peptides. The results show that fragmentation occurs by similar channels in both activation methods, but that the branching ratios are vastly different. Observation of a size-dependent minimum laser pulse energy required to induce fragmentation, and collisional cooling rates in time resolved experiments show that laser-induced dissociation occurs through the absorption of multiple photons by the chromophore and the subsequent heating through vibrational energy redistribution. The differences in branching ratio between collision- and laser-induced dissociation can then be understood by the highly anisotropic energy distribution following absorption of a photon.

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Action-FRET of a Gaseous Protein

Mass spectrometry is an extremely powerful technique for analysis of biological molecules, in particular proteins. One aspect that has been contentious is how much native solution-phase structure is preserved upon transposition to the gas phase by soft ionization methods such as electrospray ionization. To address this question—and thus further develop mass spectrometry as a tool for structural biology—structure-sensitive techniques must be developed to probe the gas-phase conformations of proteins. Here, we report Förster resonance energy transfer (FRET) measurements on a ubiquitin mutant using specific photofragmentation as a reporter of the FRET efficiency. The FRET data is interpreted in the context of circular dichroism, molecular dynamics simulation, and ion mobility data. Both the dependence of the FRET efficiency on the charge state—where a systematic decrease is observed—and on methanol concentration are considered. In the latter case, a decrease in FRET efficiency with methanol concentration is taken as evidence that the conformational ensemble of gaseous protein cations retains a memory of the solution phase conformational ensemble upon electrospray ionization.

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Carboxylated,Fe‐Filled Multiwalled Carbon Nanotubes as Versatile Catalysts for O2 Reduction and H2 Evolution Reactions at Physiological pH

The development of new electrocatalysts for the oxygen reduction reaction (ORR) and hydrogen evolution reaction (HER) at physiological pH is critical for several fields, including fuel cells and biological applications. Herein, the assembly of an electrode based on carboxyl‐functionalised hydrophilic multiwalled carbon nanotubes (MWCNTs) filled with Fe phases and their excellent performance as electrocatalysts for ORR and HER at physiological pH are reported. The encapsulated Fe dramatically enhances the catalytic activity, and the graphitic shells play a double role of efficiently mediating the electron transfer to O₂ and H₂O reactants and providing a cocoon that prevents uncontrolled Fe oxidation or leaching.     

Cobalt‐Mediated Radical Polymerization of Vinyl Acetate and Acrylonitrile in Supercritical Carbon Dioxide

Cobalt‐mediated radical polymerization (CMRP) of vinyl acetate (VAc) is successfully achieved in supercritical carbon dioxide (scCO₂). CMRP of VAc is conducted using an alkyl‐cobalt(III) adduct that is soluble in scCO₂. Kinetics studies coupled to visual observations of the polymerization medium highlight that the melt viscosity and PVAc molar mass (M_n) are key parameters that affect the CMRP in scCO₂. It is noticed that CMRP is controlled for M_n up to 10 000 g mol⁻¹, but loss of control is progressively observed for higher molar masses when PVAc precipitates in the polymerization medium. Low molar mass PVAc macroinitiator, prepared by CMRP in scCO₂, is then successfully used to initiate the acrylonitrile polymerization. PVAc‐b‐PAN block copolymer is collected as a free flowing powder at the end of the process although the dispersity of the copolymer increases with the reaction time. Although optimization is required to decrease the dispersity of the polymer formed, this CMRP process opens new perspectives for macromolecular engineering in scCO₂ without the utilization of fluorinated comonomers or organic solvents.

     

Bounded Correctors in Almost Periodic Homogenization

We show that certain linear elliptic equations (and systems) in divergence form with almost periodic coefficients have bounded, almost periodic correctors. This is proved under a new condition we introduce which quantifies the almost periodic assumption and includes (but is not restricted to) the class of smooth, quasiperiodic coefficient fields which satisfy a Diophantine-type condition previously considered by Kozlov (Mat Sb (N.S), 107(149):199–217, 1978). The proof is based on a quantitative ergodic theorem for almost periodic functions combined with the new regularity theory recently introduced by Armstrong and Shen (Pure Appl Math, 2016) for equations with almost periodic coefficients. This yields control on spatial averages of the gradient of the corrector, which is converted into estimates on the size of the corrector itself via a multiscale Poincaré-type inequality.     

h-Principles for the Incompressible Euler Equations

In Dissipative Euler Flows and Onsager’s Conjecture. arxiv.1205.3626, preprint, 2012, De Lellis and Székelyhidi construct Hölder continuous, dissipative (weak) solutions to the incompressible Euler equations in the torus ${{\mathbb T}^3}$ . The construction consists of adding fast oscillations to the trivial solution. We extend this result by establishing optimal h-principles in two and three space dimensions. Specifically, we identify all subsolutions (defined in a suitable sense) which can be approximated in the H ^?1-norm by exact solutions. Furthermore, we prove that the flows thus constructed on ${{\mathbb T}^3}$ are genuinely three-dimensional and are not trivially obtained from solutions on ${{\mathbb T}^2}$ .     

Synthesis and multinuclear NMR characterization of iminophosphoranyl phosphines and silanes

Tris(iminotriphenylphosphoranyl)phosphonium chloride 2 , tris(iminotriphenylphosphoranyl)phosphine 3 , bis(iminotriphenylphosphoranyl)dichlorosilane 4 , tris(iminotriphenylphosphoranyl)-chlorosilane 5 and -hydrogenosilane 6 have been prepared by reacting the iminotriphenylphosphorane 1 with trichlorophosphine or the corresponding chlorosilanes. A multinuclear NMR study of these compounds is presented. © 1996 John Wiley & Sons, Inc.