Efficient Disproportionation of Formic Acid to Methanol Using Molecular Ruthenium Catalysts

The disproportionation of formic acid to methanol was unveiled in 2013 using iridium catalysts. Although attractive, this transformation suffers from very low yields; methanol was produced in less than 2 % yield, because the competitive dehydrogenation of formic acid (to CO₂ and H₂) is favored. We report herein the efficient and selective conversion of HCOOH to methanol in 50 % yield, utilizing ruthenium(II) phosphine complexes under mild conditions. Experimental and theoretical (DFT) results show that different convergent pathways are involved in the production of methanol, depending on the nature of the catalyst. Reaction intermediates have been isolated and fully characterized and the reaction chemistry of the resulting ruthenium complexes has been studied.     

Eco-friendly synthesis of esters under ultrasound with p-toluenesulfonic acid as catalyst

The present work describes the efficient ultrasound-assisted synthesis of saturated aliphatic esters from synthetic aliphatic acids in methanol or in ethanol, using p-toluenesulfonic acid as a catalyst. The esters were isolated in good yields after short reaction times under mild conditions. The compounds were analyzed by high resolution mass spectrometry (HRMS), which give a fragmentations pathway common for these molecules.     

Momentum‐based approximation of incompressible multiphase fluid flows

We introduce a time stepping technique using the momentum as dependent variable to solve incompressible multiphase problems. The main advantage of this approach is that the mass matrix is time‐independent making this technique suitable for spectral methods. A level set method is applied to reconstruct the fluid properties such as density. We also introduce a stabilization method using an entropy‐viscosity technique and a compression technique to limit the flattening of the level set function. We extend our algorithm to immiscible conducting fluids by coupling the incompressible Navier‐Stokes and the Maxwell equations. We validate the proposed algorithm against analytical and manufactured solutions. Results on test cases such as Newton's bucket problem and a variation thereof are provided. Surface tension effects are tested on benchmark problems involving bubbles. A numerical simulation of a phenomenon related to the industrial production of aluminium is presented at the end of the paper.     

On Kerckhoff Minima and Pleating Loci for Quasi-Fuchsian Groups

We show how Kerckhoff's results on minima of length functions on Teichmüller space can be used to analyse the possible bending loci of the boundary of the convex hull for quasi-Fuchsian groups near to the Fuchsian locus.     

The Stokes phenomenon in the confluence of the hypergeometric equation using Riccati equation

In this paper we study the confluence of two regular singular points of the hypergeometric equation into an irregular one. We study the consequence of the divergence of solutions at the irregular singular point for the unfolded system. Our study covers a full neighborhood of the origin in the confluence parameter space. In particular, we show how the divergence of solutions at the irregular singular point explains the presence of logarithmic terms in the solutions at a regular singular point of the unfolded system. For this study, we consider values of the confluence parameter taken in two sectors covering the complex plane. In each sector, we study the monodromy of a first integral of a Riccati system related to the hypergeometric equation. Then, on each sector, we include the presence of logarithmic terms into a continuous phenomenon and view a Stokes multiplier related to a 1-summable solution as the limit of an obstruction that prevents a pair of eigenvectors of the monodromy operators, one at each singular point, to coincide.     

Development of an advanced on‐line position‐specific stable carbon isotope system and application to methyl tert‐butyl ether

We present an advanced system for on‐line position‐specific carbon isotope analysis. The main limitation of on‐line intramolecular isotope ratio measurements has been that optimal pyrolytic fragments are obtained mostly at temperatures where the analyte has not completely reacted. As a result of undetermined isotopic fractionation, the isotopic signatures of the pyrolysis products are not strictly equal to these of the equivalent moieties in the parent molecule. We designed a pyrolytic unit in which both temperature and reaction time are variable parameters, enabling determination of the enrichment factor of the pyrolysis at optimal temperature by construction of a Rayleigh plot. In the case of methyl tert‐butyl ether (MTBE) presented here, a ‘pre‐pyrolysis’ fractionation of MTBE leading to a depletion of 0.9‰ was discovered and the enrichment factor of the optimal pyrolysis reaction was determined at −1.7‰. Absolute δ¹³C values of two functional groups of MTBE – the methoxy group and the 2‐methylpropane group – could be determined with 95% confidence intervals of 0.4‰ and 0.5‰, respectively. Copyright © 2009 John Wiley & Sons, Ltd.     

(2RS,5SR,6SR)‐Methyl 4‐{cis‐2‐[3‐fluoro‐5‐(4‐methoxy‐3,4,5,6‐tetrahydro‐2H‐pyran‐4‐yl)phenoxy­methyl]‐6‐hydroxy‐3‐phenylmorpholino}­benzene­sulfinate

The title compound, C₃₀H₃₄FNO₇S, is a key inter­mediate in the design of dual 5‐LOX (5‐lipoxygenase)/COX‐2 (cyclo­oxygenase‐2) inhibitors. The compound crystallizes as a racemate. Linear hydrogen‐bonded chains are aligned along the [201] direction, and stacked π–π inter­actions and C—H⋯O contacts stabilize the crystal structure.     

Cyclic coverings and higher order embeddings of algebraic varieties

In the present paper we study higher order embeddings in the context of cyclic coverings. Analyzing the positivity of the line bundle downstairs and its relationship with the branch divisor, we provide criteria for its pull-back to define an embedding of given order. We show that the obtained criteria are sharp. Finally, we apply them to various - sometimes seemingly unrelated-problems in algebraic geometry.