Singular solutions for the constant Q-curvature problem

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.     

Hyperpositive non-linear effects: enantiodivergence and modelling

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 k_obs 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 k_obs 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.     

From the N‐Heterocyclic Carbene‐Catalyzed Conjugate Addition of Alcohols to the Controlled Polymerization of (Meth)acrylates

Among various N‐heterocyclic carbenes (NHCs) tested, only 1,3‐bis(tert‐butyl)imidazol‐2‐ylidene (NHC^tBu) proved to selectively promote the catalytic conjugate addition of alcohols onto (meth)acrylate substrates. This rather rare example of NHC‐catalyzed 1,4‐addition of alcohols was investigated as a simple means to trigger the polymerization of both methyl methacrylate and methyl acrylate (MMA and MA, respectively). Well‐defined α‐alkoxy poly(methyl (meth)acrylate) (PM(M)A) chains, the molar masses of which could be controlled by the initial [(meth)acrylate]₀/[ROH]₀ molar ratio, were ultimately obtained in N,N‐dimethylformamide at 25 °C. A hydroxyl‐terminated poly(ethylene oxide) (PEO‐OH) macro‐initiator was also employed to directly access PEO‐b‐PMMA amphiphilic block copolymers. Investigations into the reaction mechanism by DFT calculations revealed the occurrence of two competitive concerted pathways, involving either the activation of the alcohol or that of the monomer by NHC^tBu.     

A Switch in the Hydrophobic/Hydrophilic Gas-Adsorption Character of Prussian Blue Analogues: An Affinity Control for Smart Gas Sorption

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.     

ESTIMATION OF PARAMETERS IN A CLOSED PYGMY POPULATION IN CAMEROON

Inspired by Kouakep [16], we consider in this note a wellposed model with differential susceptibility and infectivity adding continuous age structure to an ODE model for a "Baka" pygmy group in the East of Cameroon(Africa).Assuming a very low contribution of carriers to infection compared to acute infection, we estimate a probability p(a)(to develop symptomatic Hepatitis B state at age a) and acute carriers' transmission rate. The value R_0= 2:67 1 of the basic reproduction number estimated from data in the east of Cameroon confirms that HBV is endemic in the Baka pygmy group.     

ToF-S-SIMS molecular 3D analysis of micro-objects as an alternative to ion beam erosion at large depth: application to single inkjet dots

Molecular depth profiling is needed to develop high-tech materials optimised to the μm or even up to the nm scale. Recent progress in time-of-flight static secondary ion mass spectrometry (ToF-S-SIMS) offers perspectives to molecular depth profiling. However, at this moment, the methodology is not yet capable to deal with a range of materials science applications because of the limited depth range, the loss of intensity in the subsurface and the loss of depth resolution at large distances from the original surface. Therefore, the purpose of this paper is to develop a complementary approach for the molecular 3D analysis at large depth, using a combination of ultra-low angle microtomy (ULAM) and surface analysis of the sectioned material with ToF-S-SIMS. Single inkjet dots with a diameter of 100 μm and height of 22 μm on a PET substrate have been used as a test system for the methodology. It is demonstrated that the use of a diamond knife allows the molecular composition and distribution of components within the microscopic feature to be probed with a lateral resolution of 300 nm. Hence the methodology approaches the physical limit for ion imaging of organic components with local concentrations in the % range. In practice, the achievable depth resolution with ULAM-S-SIMS is ultimately limited by the surface roughness of the section. Careful optimisation of the ULAM step has resulted in a surface roughness within 6 nm (R _a value) at a depth of 21 μm. This offers perspective to achieve 3D analysis with a depth resolution as good as 18 nm at such a large distance from the surface. Furthermore, the ULAM-S-SIMS approach is applicable to materials unamenable to ion beam erosion. However, the method is limited to dealing with, for instance, Si or glass substrates that cannot be sectioned with a microtomy knife. Furthermore, sufficient adhesion between stacked layers or between the coating and substrate is required. However, it is found that the approach is applicable to a wide variety of industrially important (multi)layers of polymers on a polymer substrate.