Stability conditions in families

Publications mathématiques de l'IHÉS - We develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based...     

Parton distributions and new physics searches: the Drell–Yan forward–backward asymmetry as a case study

We present the first unquenched lattice-QCD calculation of the form factors for the decay \(B\rightarrow D^*\ell \nu \) at nonzero recoil. Our analysis includes 15 MILC ensembles with \(N_f=2+1\) flavors of asqtad sea quarks, with a strange quark mass close to its physical mass. The lattice spacings range from \(a\approx 0.15\) fm down to 0.045 fm, while the ratio between the light- and the strange-quark masses ranges from 0.05 to 0.4. The valence b and c quarks are treated using the Wilson-clover action with the Fermilab interpretation, whereas the light sector employs asqtad staggered fermions. We extrapolate our results to the physical point in the continuum limit using rooted staggered heavy-light meson chiral perturbation theory. Then we apply a model-independent parametrization to extend the form factors to the full kinematic range. With this parametrization we perform a joint lattice-QCD/experiment fit using several experimental datasets to determine the CKM matrix element \(|V_{cb}|\). We obtain \(\left| V_{cb}\right| = (38.40 \pm 0.68_{\text {th}} \pm 0.34_{\text {exp}} \pm 0.18_{\text {EM}})\times 10^{-3}\). The first error is theoretical, the second comes from experiment and the last one includes electromagnetic and electroweak uncertainties, with an overall \(\chi ^2\text {/dof} = 126/84\), which illustrates the tensions between the experimental data sets, and between theory and experiment. This result is in agreement with previous exclusive determinations, but the tension with the inclusive determination remains. Finally, we integrate the differential decay rate obtained solely from lattice data to predict \(R(D^*) = 0.265 \pm 0.013\), which confirms the current tension between theory and experiment.

     

A Dual Photoredox- and Cp2TiCl2-Catalyzed Approach for the Direct Access to α-Vinyl-β-hydroxy Esters

For the first time, a dual photoredox- and titanocene-catalyzed methodology for the regioselective access to α-vinyl-β-hydroxy esters towards aldehyde allylation with 4-bromobut-2-enoate is reported. The protocol is based on the Barbier-type properties of the inexpensive and available Cp₂TiCl₂ in catalytic amount (5 mol%). The developed mild reaction conditions gave access to a library of differently functionalized α-vinyl-β-hydroxy esters in moderate diastereoselectivity, employing the commercially available ethyl 4-bromobut-2-enoate and both aromatic and aliphatic aldehydes. The reaction was realized under visible light irradiation, in the presence of an organophotocatalyst (3DPAFIPN, 2 mol%) combined with Hantzsch's ester as the sacrificial reductant. In contrast to other Barbier-type reactions employing ethyl 4-bromobut-2-enoate, the photoredox system ensures a better regioselectivity. Moreover, the use of preformed organometallic nucleophilic species (e. g., dienolborinates), and the need of metal reductants or stoichiometric amount of transition metals in low oxidation state for Barbier-type reactions, is avoided. To support the experimental evidence, a detailed photophysical study shed light on the mechanism of the reaction.     

Similar Structural Dynamics for the Degradation of CH3NH3PbI3 in Air and in Vacuum

We investigate the degradation path of MAPbI₃ (MA=methylammonium) films over flat TiO₂ substrates at room temperature by means of X‐ray diffraction, spectroscopic ellipsometry, X‐ray photoelectron spectroscopy, and high‐resolution transmission electron microscopy. The degradation dynamics is found to be similar in air and under vacuum conditions, which leads to the conclusion that the occurrence of intrinsic thermodynamic mechanisms is not necessarily linked to humidity. The process has an early stage, which drives the starting tetragonal lattice in the direction of a cubic atomic arrangement. This early stage is followed by a phase change towards PbI₂. We describe how this degradation product is structurally coupled with the original MAPbI₃ lattice through the orientation of its constituent PbI₆ octahedra. Our results suggest a slight octahedral rearrangement after volatilization of HI+CH₃NH₂ or MAI, with a relatively low energy cost. Our experiments also clarify why reducing the interfaces and internal defects in the perovskite lattice enhances the stability of the material.     

Mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with non-smooth coefficients

We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with low regularity of the coefficients. We then use them to prove the parabolic strong maximum principle and the parabolic Harnack inequality. We emphasize that our results only rely on the classical theory, and our arguments follow the lines used in the original theory of harmonic functions. We provide two proofs relying on two different formulations of the divergence theorem, one stated for sets with almost C¹-boundary, the other stated for sets with finite perimeter.     

Direct flow injection profiling of acyl glycerols from food products using isopropanol as solvent

This work proposes a novel method for the direct flow injection profiling of acylglycerols in edible oils and fats without preliminary extraction and consequent reconstitution in the injection solvent. The work exploits the outstanding performance of high‐resolution mass spectrometry to target unique elemental compositions even in the most complex matrices. The performance of isopropanol as the unique solvent for both the solubilization and analysis of acylglycerols was investigated in comparison with other classical methods involving preliminary extractions, sample recovery, and analysis. The calibrations of two triglyceride standards (triolein and trilinolenin) were successfully performed in presence and absence of oil matrix. As final application, the effects on the acylglycerol fraction of a heat treatment on three different fat samples (extra virgin olive oil, lard oil, and fat from dry cured ham—speck) were monitored. The proposed method is therefore suitable for a rapid evaluation of acylglycerol fractions in food lipid samples.