Sparse approximate solutions to stochastic Galerkin equations

In this Note, we formulate a sparse Krylov-based algorithm for solving large-scale linear systems of algebraic equations arising from the discretization of randomly parametrized (or stochastic) elliptic partial differential equations (SPDEs). We analyze the proposed sparse conjugate gradient (CG) algorithm within the framework of inexact Krylov subspace methods, prove its convergence and study its abstract computational cost. Numerical studies conducted on stochastic diffusion models show that the proposed sparse CG algorithm outperforms the classical CG method when the sought solutions admit a sparse representation in a polynomial chaos basis. In such cases, the sparse CG algorithm recovers almost exactly the sparsity pattern of the exact solutions, which enables accelerated convergence. In the case when the SPDE solution does not admit a sparse representation, the convergence of the proposed algorithm is very similar to the classical CG method.     

Silica-Supported MnII Sites as Efficient Catalysts for Carbonyl Hydroboration,Hydrosilylation, and Transesterification

Manganese, the third most abundant transition-metal element after iron and titanium, has recently been demonstrated to be an effective homogeneous catalyst in numerous reactions. Herein, the preparation of silica-supported Mn^II sites is reported using Surface Organometallic Chemistry (SOMC), combined with tailored thermolytic molecular precursors approach based on Mn₂[OSi(OtBu)₃]₄ and Mn{N(SiMe₃)₂}₂⋅THF. These supported Mn^II sites, free of organic ligands, efficiently catalyze numerous reactions: hydroboration and hydrosilylation of ketones and aldehydes as well as the transesterification of industrially relevant substrates.     

Detection of individual insulating entities by electrochemical blocking

Electrochemical blocking is a type of single-entity electrochemical measurement particularly well adapted to the detection of insulating particles. The digital detection of ultralow concentrations of artificial entities such as polymer particles or biotargets such as proteins and bacteria represents an exceptional opportunity for sensing applications. In this review, we explore the latest development in the field of electrochemical blocking and propose some perspectives.     

Analytical prediction of delayed Hopf bifurcations in a simplified stochastic model of reed musical instruments

Nonlinear Dynamics - This paper investigates the dynamic behavior of a simplified single reed instrument model subject to a stochastic forcing of white noise type when one of its bifurcation...     

Thermo‐ and pH‐sensitive triblock copolymers with tunable hydrophilic/hydrophobic properties

Polymers consisting of poly(acrylic acid) (PAA) and statistical poly[(acrylic acid)‐co‐(tert‐butylacrylate)] (P(AA‐co‐tBA)), attached to both extremities of Jeffamine® (D series based on a poly(propylene oxide) (PPO) with one amine function at each end) using atom transfer radical polymerization (ATRP) are presented in this article. An original bifunctional amide‐based macroinitiator was first elaborated from Jeffamine®. tBA polymerization was subsequently initiated from this macroinitiator. This polymerization occurs in a well‐controlled manner leading to narrow molecular weights distribution. Amphiphilic copolymers were finally obtained after complete or partial hydrolysis of the PtBA blocks into PAA. The control of the partial hydrolysis of tBA units, conducted in a concentrated HCl/tetrahydrofuran mixture, is demonstrated. The properties of the triblock copolymers were preliminary investigated in aqueous solution by absorbance, DLS measurements and SEC/MALS/DV/DRI analysis as a function of temperature and pH modifications, providing evidences of thermo‐ and pH‐sensitive self‐assembly of the copolymers. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2606–2616     

Synthesis,Electrochemistry, and Photophysics of Aza‐BODIPY Porphyrin Dyes

The synthesis of dyad and triad aza‐BODIPY‐porphyrin systems in two steps starting from an aryl‐substituted aza‐BODIPY chromophore is described. The properties of the resulting aza‐BODIPY‐porphyrin conjugates have been extensively investigated by means of electrochemistry, spectroelectrochemistry, and absorption/emission spectroscopy. Fluorescence measurements have revealed a dramatic loss of luminescence intensity, mainly due to competitive energy transfer and photoinduced electron transfer involving charge separation followed by recombination.     

Radical Cyclisation of α‐Halo Aluminium Acetals: A Mechanistic Study

α‐Bromo aluminium acetals are suitable substrates for Ueno–Stork‐like radical cyclisations affording γ‐lactols and acid‐sensitive methylene‐γ‐lactols in high yields. The mechanistic study herein sets the scope and limitation of this reaction. The influence of the halide (or chalcogenide) atom X (X=Cl, Br, I, SPh, SePh) in the precursors α‐haloesters, as well as influence of the solvent and temperature was studied. The structure of the aluminium acetal intermediates resulting from the reduction of the corresponding α‐haloesters has been investigated by low‐temperature ¹³C‐INEPT diffusion‐ordered NMR spectroscopy (DOSY) experiments and quantum calculations, providing new insights into the structures of these thermally labile intermediates. Oxygen‐bridged dimeric structures with a planar Al₂O₂ ring are proposed for the least hindered aluminium acetals, while monomeric structures seem to prevail for the most hindered species. A comparison against the radical cyclisation of aluminium acetals derived from allyl and propargyl alcohols with the parent Ueno–Stork has been made at the BHandHLYP/6‐311++G(d,p) level of theory, highlighting mechanistic similarities and differences.     

Ergodic theorems with arithmetical weights

We prove that the divisor function d(n) counting the number of divisors of the integer n is a good weighting function for the pointwise ergodic theorem. For any measurable dynamical system (X, A, ν, τ) and any f ∈ L ^p (ν), p > 1, the limit

$$\mathop {\lim }\limits_{n \to \infty } \frac{1}{{\Sigma _{k = 1}^nd\left( k \right)}}\sum\limits_{k = 1}^n {d\left( k \right)f\left( {{\tau ^k}x} \right)} $$

exists ν-almost everywhere. The proof is based on Bourgain’s method, namely the circle method based on the shift model. Using more elementary ideas we also obtain similar results for other arithmetical functions, like the θ(n) function counting the number of squarefree divisors of n and the generalized Euler totient function J _s (n) = Σ _d|n d ^s μ(n/d), s > 0.

     

Modelling the voltammetry of adsorbed enzymes and molecular catalysts

When redox enzymes are attached to electrodes and undergo direct electron transfer, their voltammetric responses exhibit diverse shapes that, if analysed correctly, may inform about various aspects of the catalytic mechanism. Here we review the models that have been proposed to interpret these signals in relation to the thermodynamics and kinetics of interfacial and intramolecular electron transfer and active site chemistry. We list the corresponding equations in forms that are ready to use for fitting, and the commands that run these fits in the open source software QSoas. We relate these models to those that have been used for characterizing small synthetic redox catalysts diffusing in solution.