This paper is devoted to the construction of weak solutions to the singular constant Q-curvature problem. We build on several tools developed in the last years. This is the first construction of singular metrics on closed manifolds of sufficiently large dimension with constant (positive) Q-curvature. 相似文献
We establish Hölder continuity of the horizontal gradient of weak solutions to quasi-linear $p$-Laplacian type non-homogeneous equations in the Heisenberg Group. 相似文献
Sulfite is often added to beverages as an antioxidant and antimicrobial agent. In fermented beverages, sulfite is also naturally produced by yeast cells. However, sulfite causes adverse health effects in asthmatic patients and accurate measurement of the sulfite concentration is therefore very important. Current sulfite analysis methods are time- and reagent-consuming and often require costly equipment. Here, we present a system allowing sensitive, ultralow-volume sulfite measurements based on a reusable glass-silicon microdroplet platform on which microdroplet generation, addition of enzymes through chemical-induced emulsion destabilization and pillar-induced droplet merging, emulsion restabilization, droplet incubation, and fluorescence measurements are integrated. In a first step, we developed and verified a fluorescence-based enzymatic assay for sulfite by measuring its analytical performance (LOD, LOQ, the dynamic working range, and the influence of salts, colorant, and sugars) and comparing fluorescent microplate readouts of fermentation samples with standard colorimetric measurements using the 5,5′-dithiobis-(2-nitrobenzoic acid) assay of the standard Gallery Plus Beermaster analysis platform. Next, samples were analyzed on the microdroplet platform, which also showed good correlation with the standard colorimetric analysis. Although the presented platform does not allow stable reinjection of droplets due to the presence of a tight array of micropillars at the fluidics entrances to prevent channel clogging by dust, removing the pillars, and integrating miniaturized pumps and optics in a future design would allow to use this platform for high-throughput, automated, and portable screening of microbes, plant, or mammalian cells.
We report the dramatic impact of the addition of N-heterocyclic carbenes (NHCs) on the reactivity and selectivity of heterogeneous Ru catalysts in the context of C−H activation reactions. Using a simple and robust method, we prepared a series of new air-stable catalysts starting from commercially available Ru on carbon (Ru/C) and differently substituted NHCs. Associated with C−H deuteration processes, depending on Ru/C-NHC ratios, the chemical outcome can be controlled to a large extent. Indeed, tuning the reactivity of the Ru catalyst with NHC enabled: 1) increased chemoselectivity and the regioselectivity for the deuteration of alcohols in organic media; 2) the synthesis of fragile pharmaceutically relevant deuterated heterocycles (azine, purine) that are otherwise completely reduced using unmodified commercial catalysts; 3) the discovery of a novel reactivity for such heterogeneous Ru catalysts, namely the selective C-1 deuteration of aldehydes. 相似文献
Porous coordination polymers are molecule-based materials presenting a high degree of tunability, which offer many advantages for targeted applications over conventional inorganic materials. This work demonstrates that the hydrophilic/hydrophobic character of Prussian blue analogues having a lipophilic feature may be tuned to optimize the gas adsorption properties. The role of the coordinatively unsaturated metal sites is emphasized through a combination of theoretical and experimental study of water, ethanol, and n-hexane adsorption. 相似文献
While chemotherapy is one of the most used treatments in oncology, the systemic administration of chemotherapeutics generally results in undesired damages to healthy tissues and cells, side effects such as severe nausea and leukopenia, and reduced efficacy due to multidrug resistance and poor target accessibility. The limitations of conventional chemotherapy formulation have prompted the development of alternative nanomaterials-based strategies to achieve targeted and stimuli sensitive payload delivery to reach optimal local drug concentration at tumor sites. In this study, the anticancer drug chlorambucil (Clb) was conjugated to the surface of silica coated lithium niobate (LNO) harmonic nanoparticles (HNPs) using a photocaging tether based on coumarin-4-yl methyl derivative. Upon laser pulsed femtosecond irradiation at 790 nm, the second harmonic emission from the metal oxide core induced the efficient release of Clb, with concomitant contribution from the nonlinear absorption of the coumarin (CM)-based moiety. 相似文献
We establish local and global well-posedness of the 2D dissipative quasi-geostrophic equation in critical mixed norm Lebesgue spaces. The result demonstrates
the persistence of the anisotropic behavior of the initial data under the evolution of
the 2D dissipative quasi-geostrophic equation. The phenomenon is a priori nontrivial
due to the nonlocal structure of the equation. Our approach is based on Kato's method
using Picard's iteration, which can be adapted to the multi-dimensional case and
other nonlinear non-local equations. We develop time decay estimates for solutions of
fractional heat equation in mixed norm Lebesgue spaces that could be useful for other
problems. 相似文献
The chiral ligand N-methylephedrine (NME) was found to catalyse the addition of dimethylzinc to benzaldehyde in an enantiodivergent way, with a monomeric and a homochiral dimeric complex both catalysing the reaction at a steady state and giving opposite product enantiomers. A change in the sign of the enantiomeric product was thus possible by simply varying the catalyst loading or the ligand ee, giving rise to an enantiodivergent non-linear effect. Simulations using a mathematical model confirmed the possibility of such behaviour and showed that this can lead to situations where a reaction gives racemic products, although the system is composed only of highly enantioselective individual catalysts. Furthermore, depending on the dimer''s degree of participation in the catalytic conversion, enantiodivergence may or may not be observed experimentally, which raises questions about the possibility of enantiodivergence in other monomer/dimer-catalysed systems. Simulations of the reaction kinetics showed that the observed kinetic constant kobs is highly dependent on user-controlled parameters, such as the catalyst concentration and the ligand ee, and may thus vary in a distinct way from one experimental setup to another. This unusual dependency of kobs allowed us to confirm that a previously observed U-shaped catalyst order vs. catalyst loading-plot is linked to the simultaneous catalytic activity of both monomeric and dimeric complexes.An asymmetric reaction consisting of competing monomeric and dimeric catalysts may explain enantiodivergent non-linear effects.相似文献